Main Branches

Downloads  Installation  Overview  Data Libraries  Packages  Documentation  Contacts  FAQ  GAP 3 

117 publications using GAP in the category "Information and communication, circuits"

[AG08] Aguglia, A. and Giuzzi, L., Construction of a 3-dimensional MDS-code, Contrib. Discrete Math., 3 (1) (2008), 39–46.

[AH04] Araya, M. and Harada, M., MDS codes over $\Bbb F_9$ related to the ternary Golay code, Discrete Math., 282 (1-3) (2004), 233–237.

[AH16] Araya, M. and Harada, M., On the classification of certain ternary codes of length 12, Hiroshima Math. J., 46 (1) (2016), 87–96.

[AHK04] Araya, M., Harada, M., and Kharaghani, H., Some Hadamard matrices of order 32 and their binary codes, J. Combin. Des., 12 (2) (2004), 142–146.

[BB+16] Álvarez-Barrientos, I., Borges-Quintana, M., Borges-Trenard, M. A., and Panario, D., Computing Gröbner bases associated with lattices, Adv. Math. Commun., 10 (4) (2016), 851–860.

[X02] Östergård, P. R. J., Classifying subspaces of Hamming spaces, Des. Codes Cryptogr., 27 (3) (2002), 297–305.

[BCC08] Bailey, R. A., Cameron, P. J., and Connelly, R., Sudoku, gerechte designs, resolutions, affine space, spreads, reguli, and Hamming codes, Amer. Math. Monthly, 115 (5) (2008), 383–404.

[B09] Bailey, R. F., Error-correcting codes from permutation groups, Discrete Math., 309 (13) (2009), 4253–4265.

[B06] Bailey, R. F., Uncoverings-by-bases for base-transitive permutation groups, Des. Codes Cryptogr., 41 (2) (2006), 153–176.

[BP12] Bailey, R. F. and Prellberg, T., Decoding generalised hyperoctahahedral groups and asymptotic analysis of correctible error patterns, Contrib. Discrete Math., 7 (1) (2012), 1–14.

[B98] Barg, A., Complexity issues in coding theory, in Handbook of coding theory, Vol. I, II, North-Holland, Amsterdam (1998), 649–754.

[BD+17] Becker, P. E., Derka, M., Houghten, S., and Ulrich, J., Build a sporadic group in your basement, Amer. Math. Monthly, 124 (4) (2017), 291–305.

[BBS16] Bernal, J. J., Bueno-Carreño, D. H., and Simón, J. J., Cyclic and BCH codes whose minimum distance equals their maximum BCH bound, Adv. Math. Commun., 10 (2) (2016), 459–474.

[BS+05] Bohli, J., Steinwandt, R., González Vasco, M. I., and Martínez, C., Weak keys in $MST_1$, Des. Codes Cryptogr., 37 (3) (2005), 509–524.

[BWY16] Bouyuklieva, S., Willems, W., and Yankov, N., On the automorphisms of order 15 for a binary self-dual $[96, 48, 20]$ code, Des. Codes Cryptogr., 79 (1) (2016), 171–182.

[BR05] Britz, T. and Rutherford, C. G., Covering radii are not matroid invariants, Discrete Math., 296 (1) (2005), 117–120.

[BP09] Bulygin, S. and Pellikaan, R., Bounded distance decoding of linear error-correcting codes with Gröbner bases, J. Symbolic Comput., 44 (12) (2009), 1626–1643.

[B06] Bulygin, S. V., Generalized Hermitian codes over $\rm GF(2^r)$, IEEE Trans. Inform. Theory, 52 (10) (2006), 4664–4669.

[CC+16] Cao, Y., Cao, Y., Fu, F., and Gao, J., On a class of left metacyclic codes, IEEE Trans. Inform. Theory, 62 (12) (2016), 6786–6799.

[CO01] Caprotti, O. and Oostdijk, M., Formal and efficient primality proofs by use of computer algebra oracles, J. Symbolic Comput., 32 (1-2) (2001), 55–70
(Computer algebra and mechanized reasoning (St. Andrews, 2000)).

[CDS09] Caranti, A., Dalla Volta, F., and Sala, M., An application of the O'Nan-Scott theorem to the group generated by the round functions of an AES-like cipher, Des. Codes Cryptogr., 52 (3) (2009), 293–301.

[CIN10] Casiello, D., Indaco, L., and Nagy, G. P., On the computational approach to the problem of the existence of a projective plane of order 10, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia, 57 (2010), 69–88 (2011).

[CK15] Cavallo, B. and Kahrobaei, D., Secret sharing using non-commutative groups and the shortlex order, in Algorithmic problems of group theory, their complexity, and applications to cryptography, Amer. Math. Soc., Providence, RI, Contemp. Math., 633 (2015), 1–8.

[CP95] Charnes, C. and Pieprzyk, J., Attacking the $\rm SL_2$ hashing scheme, in Advances in cryptology—ASIACRYPT '94 (Wollongong, 1994), Springer, Berlin, Lecture Notes in Comput. Sci., 917 (1995), 322–330.

[CRB02] Charnes, C., Rötteler, M., and Beth, T., Homogeneous bent functions, invariants, and designs, Des. Codes Cryptogr., 26 (1-3) (2002), 139–154
(In honour of Ronald C. Mullin).

[CD15] Chen, B. and Dinh, H. Q., Equivalence classes and structures of constacyclic codes over finite fields, in Algebra for secure and reliable communication modeling, Amer. Math. Soc., Providence, RI, Contemp. Math., 642 (2015), 181–223.

[CF+12] Chen, B., Fan, Y., Lin, L., and Liu, H., Constacyclic codes over finite fields, Finite Fields Appl., 18 (6) (2012), 1217–1231.

[CLL17] Chen, B., Lin, L., and Ling, S., External difference families from finite fields, J. Combin. Des., 25 (1) (2017), 36–48.

[CR16] Craven, M. J. and Robertz, D., A parallel evolutionary approach to solving systems of equations in polycyclic groups, Groups Complex. Cryptol., 8 (2) (2016), 109–125.

[CMR10] Crnković, D., Mikulić, V., and Rodrigues, B. G., Some strongly regular graphs and self-orthogonal codes from the unitary group $\rm U_4(3)$, Glas. Mat. Ser. III, 45(65) (2) (2010), 307–323.

[CR13] Crnković, D. and Rodrigues, B. G., Self-orthogonal codes from some Bush-type Hadamard matrices, Quaest. Math., 36 (3) (2013), 341–352.

[DG+09] De Beule, J., Govaerts, P., Hallez, A., and Storme, L., Tight sets, weighted $m$-covers, weighted $m$-ovoids, and minihypers, Des. Codes Cryptogr., 50 (2) (2009), 187–201.

[DF+14] Delgado, M., Farrán, J. I., García-Sánchez, P. A., and Llena, D., On the weight hierarchy of codes coming from semigroups with two generators, IEEE Trans. Inform. Theory, 60 (1) (2014), 282–295.

[D06] Dempwolff, U., Automorphisms and equivalence of bent functions and of difference sets in elementary abelian 2-groups, Comm. Algebra, 34 (3) (2006), 1077–1131.

[D12] Dukes, P. J., Coding with injections, Des. Codes Cryptogr., 65 (3) (2012), 213–222.

[EP01] Egner, S. and Püschel, M., Automatic generation of fast discrete signal transforms, IEEE Trans. Signal Process., 49 (9) (2001), 1992–2002.

[EP04] Egner, S. and Püschel, M., Symmetry-based matrix factorization, J. Symbolic Comput., 37 (2) (2004), 157–186.

[E05] Eick, B., Computational group theory, Jahresber. Deutsch. Math.-Verein., 107 (3) (2005), 155–170.

[EG+08] Estrada, S., García-Rozas, J. R., Peralta, J., and Sánchez-García, E., Group convolutional codes, Adv. Math. Commun., 2 (1) (2008), 83–94.

[FG15] Farrán, J. I. and García-Sánchez, P. A., The second Feng-Rao number for codes coming from inductive semigroups, IEEE Trans. Inform. Theory, 61 (9) (2015), 4938–4947.

[FG+99] Fields, J. E., Gaborit, P., Huffman, W. C., and Pless, V., On the classification of extremal even formally self-dual codes, Des. Codes Cryptogr., 18 (1-3) (1999), 125–148
(Designs and codes—a memorial tribute to Ed Assmus).

[FG+01] Fields, J. E., Gaborit, P., Huffman, W. C., and Pless, V., On the classification of extremal even formally self-dual codes of lengths 20 and 22, Discrete Appl. Math., 111 (1-2) (2001), 75–86.

[F05] Fripertinger, H., Enumeration of the semilinear isometry classes of linear codes, Bayreuth. Math. Schr. (74) (2005), 100–122.

[GKL15] Garber, D., Kahrobaei, D., and Lam, H. T., Length-based attacks in polycyclic groups, J. Math. Cryptol., 9 (1) (2015), 33–43.

[GG+13] García Pillado, C., González, S., Martínez, C., Markov, V., and Nechaev, A., Group codes over non-abelian groups, J. Algebra Appl., 12 (7) (2013), 1350037, 20.

[GG+15] Garsia-Pilʹyado, K., Gonsales, S., Markov, V. T., and Martines, K., Nonabelian group codes over an arbitrary finite field, Fundam. Prikl. Mat., 20 (1) (2015), 17–22.

[GG+12] Garsia-Pilʹyado, K., Gonsales, S., Markov, V. T., Martines, K., and Nechaev, A. A., When are all group codes of a noncommutative group abelian (a computational approach)?, Fundam. Prikl. Mat., 17 (2) (2011/12), 75–85.

[G05] Gebhardt, V., A new approach to the conjugacy problem in Garside groups, J. Algebra, 292 (1) (2005), 282–302.

[GPS15] Gillespie, N. I., Praeger, C. E., and Spiga, P., Twisted permutation codes, J. Group Theory, 18 (3) (2015), 407–433.

[GAE07] Gross, D., Audenaert, K., and Eisert, J., Evenly distributed unitaries: on the structure of unitary designs, J. Math. Phys., 48 (5) (2007), 052104, 22.

[HK05] Haanpää, H. and Kaski, P., The near resolvable $2$-$(13,4,3)$ designs and thirteen-player whist tournaments, Des. Codes Cryptogr., 35 (3) (2005), 271–285.

[HK02] Haemers, W. H. and Kuijken, E., The Hermitian two-graph and its code, Linear Algebra Appl., 356 (2002), 79–93
(Special issue on algebraic graph theory (Edinburgh, 2001)).

[H97] Hiss, G., On the incidence matrix of the Ree unital, Des. Codes Cryptogr., 10 (1) (1997), 57–62.

[H04] Holmes, P. E., On minimal factorisations of sporadic groups, Experiment. Math., 13 (4) (2004), 435–440.

[H95] Horváth, Á. G., On a problem connected with the weight distribution of the Reed-Muller code of order $R$, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 38 (1995), 171–176.

[HKP10] Huang, P., Ke, W., and Pilz, G. F., The cardinality of some symmetric differences, Proc. Amer. Math. Soc., 138 (3) (2010), 787–797.

[H13] Huffman, W. C., Self-dual $\Bbb F_q$-linear $\Bbb F_q^t$-codes with an automorphism of prime order, Adv. Math. Commun., 7 (1) (2013), 57–90.

[H09] Huffman, W. C., Self-dual codes over $\Bbb F_2+u\Bbb F_2$ with an automorphism of odd order, Finite Fields Appl., 15 (3) (2009), 277–293.

[H08] Huffman, W. C., Additive cyclic codes over $\Bbb F_4$, Adv. Math. Commun., 2 (3) (2008), 309–343.

[H07] Huffman, W. C., On the decomposition of self-dual codes over $\Bbb F_2+u\Bbb F_2$ with an automorphism of odd prime order, Finite Fields Appl., 13 (3) (2007), 681–712.

[H07] Huffman, W. C., Additive cyclic codes over $\Bbb F_4$, Adv. Math. Commun., 1 (4) (2007), 427–459.

[H07] Huffman, W. C., Additive self-dual codes over $\Bbb F_4$ with an automorphism of odd prime order, Adv. Math. Commun., 1 (3) (2007), 357–398.

[H13] Huffman, W. C., On the theory of $\Bbb F_q$-linear $\Bbb F_q^t$-codes, Adv. Math. Commun., 7 (3) (2013), 349–378.

[H95] Huffman, W. C., The automorphism groups of the generalized quadratic residue codes, IEEE Trans. Inform. Theory, 41 (2) (1995), 378–386.

[HH14] Hurley, B. and Hurley, T., Systems of MDS codes from units and idempotents, Discrete Math., 335 (2014), 81–91.

[J04] Joyner, D., Toric codes over finite fields, Appl. Algebra Engrg. Comm. Comput., 15 (1) (2004), 63–79.

[JK06] Joyner, D. and Ksir, A., Automorphism groups of some AG codes, IEEE Trans. Inform. Theory, 52 (7) (2006), 3325–3329.

[KTT12] Kalka, A., Teicher, M., and Tsaban, B., Short expressions of permutations as products and cryptanalysis of the Algebraic Eraser, Adv. in Appl. Math., 49 (1) (2012), 57–76.

[KMM06] Key, J. D., McDonough, T. P., and Mavron, V. C., Information sets and partial permutation decoding for codes from finite geometries, Finite Fields Appl., 12 (2) (2006), 232–247.

[KMM05] Key, J. D., McDonough, T. P., and Mavron, V. C., Partial permutation decoding for codes from finite planes, European J. Combin., 26 (5) (2005), 665–682.

[KMM09] Key, J. D., McDonough, T. P., and Mavron, V. C., An upper bound for the minimum weight of the dual codes of Desarguesian planes, European J. Combin., 30 (1) (2009), 220–229.

[KMM17] Key, J. D., McDonough, T. P., and Mavron, V. C., Codes from Hall planes of odd order, Adv. Math. Commun., 11 (1) (2017), 179–185.

[KMM17] Key, J. D., McDonough, T. P., and Mavron, V. C., Improved partial permutation decoding for Reed-Muller codes, Discrete Math., 340 (4) (2017), 722–728.

[KKW18] Kiermaier, M., Kurz, S., and Wassermann, A., The order of the automorphism group of a binary $q$-analog of the Fano plane is at most two, Des. Codes Cryptogr., 86 (2) (2018), 239–250.

[KR03] Klappenecker, A. and Rötteler, M., Unitary error bases: constructions, equivalence, and applications, in Applied algebra, algebraic algorithms and error-correcting codes (Toulouse, 2003), Springer, Berlin, Lecture Notes in Comput. Sci., 2643 (2003), 139–149.

[KR02] Klappenecker, A. and Rötteler, M., Beyond stabilizer codes. I. Nice error bases, IEEE Trans. Inform. Theory, 48 (8) (2002), 2392–2395.

[KS15] Knapp, W. and Schaeffer, H., On the codes related to the Higman-Sims graph, Electron. J. Combin., 22 (1) (2015), Paper 1.19, 58.

[KM00] Koolen, J. H. and Munemasa, A., Tight $2$-designs and perfect $1$-codes in Doob graphs, J. Statist. Plann. Inference, 86 (2) (2000), 505–513
(Special issue in honor of Professor Ralph Stanton).

[KN13] Korchmáros, G. and Nagy, G. P., Lower bounds on the minimum distance in Hermitian one-point differential codes, Sci. China Math., 56 (7) (2013), 1449–1455.

[KN13] Korchmáros, G. and Nagy, G. P., Hermitian codes from higher degree places, J. Pure Appl. Algebra, 217 (12) (2013), 2371–2381.

[KU15] Kotov, M. and Ushakov, A., Analysis of a certain polycyclic-group-based cryptosystem, J. Math. Cryptol., 9 (3) (2015), 161–167.

[K14] Krotov, D. S., A partition of the hypercube into maximally nonparallel Hamming codes, J. Combin. Des., 22 (4) (2014), 179–187.

[LX17] Laaksonen, A. and Östergård, P. R. J., Constructing error-correcting binary codes using transitive permutation groups, Discrete Appl. Math., 233 (2017), 65–70.

[LP16] Lane-Harvard, L. and Penttila, T., Some new two-weight ternary and quinary codes of lengths six and twelve, Adv. Math. Commun., 10 (4) (2016), 847–850.

[LST01] Lempken, W., Schröder, B., and Tiep, P. H., Symmetric squares, spherical designs, and lattice minima, J. Algebra, 240 (1) (2001), 185–208
(With an appendix by Christine Bachoc and Tiep).

[LWW17] Li, C., Weber, S., and Walsh, J. M., On multi-source networks: enumeration, rate region computation, and hierarchy, IEEE Trans. Inform. Theory, 63 (11) (2017), 7283–7303.

[LP14] Liebler, R. A. and Praeger, C. E., Neighbour-transitive codes in Johnson graphs, Des. Codes Cryptogr., 73 (1) (2014), 1–25.

[LFK10] Lim, F., Fossorier, M., and Kavčić, A., Code automorphisms and permutation decoding of certain Reed-Solomon binary images, IEEE Trans. Inform. Theory, 56 (10) (2010), 5253–5273.

[MSA08] MacArthur, B. D., Sánchez-García, R. J., and Anderson, J. W., Symmetry in complex networks, Discrete Appl. Math., 156 (18) (2008), 3525–3531.

[M08] Mahalanobis, A., A simple generalization of the ElGamal cryptosystem to non-abelian groups, Comm. Algebra, 36 (10) (2008), 3878–3889.

[M08] Mahalanobis, A., The Diffie-Hellman key exchange protocol and non-abelian nilpotent groups, Israel J. Math., 165 (2008), 161–187.

[MV16] Mandić, J. and Vučičić, T., On the existence of Hadamard difference sets in groups of order 400, Adv. Math. Commun., 10 (3) (2016), 547–554.

[MTH17] Mao, W., Thill, M., and Hassibi, B., On Ingleton-violating finite groups, IEEE Trans. Inform. Theory, 63 (1) (2017), 183–200.

[M12] McLoughlin, I., A group ring construction of the [48,24,12] type II linear block code, Des. Codes Cryptogr., 63 (1) (2012), 29–41.

[MH08] McLoughlin, I. and Hurley, T., A group ring construction of the extended binary Golay code, IEEE Trans. Inform. Theory, 54 (9) (2008), 4381–4383.

[MNN06] Miri, A., Nevins, M., and Niyomsataya, T., Applications of representation theory to wireless communications, Des. Codes Cryptogr., 41 (3) (2006), 307–318.

[M14] Moori, J., Designs and codes from $PSL_2(q)$, in Group theory, combinatorics, and computing, Amer. Math. Soc., Providence, RI, Contemp. Math., 611 (2014), 137–149.

[MS17] Moori, J. and Saeidi, A., Some designs and codes invariant under the Tits group, Adv. Math. Commun., 11 (1) (2017), 77–82.

[N08] Nagy, G. P., Direct construction of code loops, Discrete Math., 308 (23) (2008), 5349–5357.

[NP15] Nakić, A. and Pavčević, M. O., Tactical decompositions of designs over finite fields, Des. Codes Cryptogr., 77 (1) (2015), 49–60.

[NP14] Neunhöffer, M. and Praeger, C. E., Sporadic neighbour-transitive codes in Johnson graphs, Des. Codes Cryptogr., 72 (1) (2014), 141–152.

[OV15] Olteanu, G. and Van Gelder, I., Construction of minimal non-abelian left group codes, Des. Codes Cryptogr., 75 (3) (2015), 359–373.

[O97] Oura, M., The dimension formula for the ring of code polynomials in genus $4$, Osaka J. Math., 34 (1) (1997), 53–72.

[OPY08] Oura, M., Poor, C., and Yuen, D. S., Towards the Siegel ring in genus four, Int. J. Number Theory, 4 (4) (2008), 563–586.

[PPC99] Park, H., Park, K., and Cho, Y., Analysis of the variable length nonzero window method for exponentiation, Comput. Math. Appl., 37 (7) (1999), 21–29.

[PM03] Püschel, M. and Moura, J. M. F., The algebraic approach to the discrete cosine and sine transforms and their fast algorithms, SIAM J. Comput., 32 (5) (2003), 1280–1316.

[PB14] Plesken, W. and Bächler, T., Counting polynomials for linear codes, hyperplane arrangements, and matroids, Doc. Math., 19 (2014), 285–312.

[PM13] Polcino Milies, C. and de Melo, F. D., On cyclic and abelian codes, IEEE Trans. Inform. Theory, 59 (11) (2013), 7314–7319.

[S10] Sawa, M., Optical orthogonal signature pattern codes with maximum collision parameter 2 and weight 4, IEEE Trans. Inform. Theory, 56 (7) (2010), 3613–3620.

[S18] Shimada, I., An even extremal lattice of rank 64, J. Number Theory, 185 (2018), 1–15.

[S00] Simonis, J., The $[23,14,5]$ Wagner code is unique, Discrete Math., 213 (1-3) (2000), 269–282
(Selected topics in discrete mathematics (Warsaw, 1996)).

[S00] Skersys, G., Computing permutation groups of error-correcting codes, Liet. Mat. Rink., 40 (Special Issue) (2000), 320–328.

[VPD10] Vasco, M. I. G., del Pozo, A. L. P., and Duarte, P. T., A note on the security of $\rm MST_3$, Des. Codes Cryptogr., 55 (2-3) (2010), 189–200.

[W01] Walker, J. L., Constructing critical indecomposable codes, IEEE Trans. Inform. Theory, 47 (5) (2001), 1780–1795.

[YAG17] Yankov, N., Anev, D., and Gürel, M., Self-dual codes with an automorphism of order 13, Adv. Math. Commun., 11 (3) (2017), 635–645.

[YL+15] Yankov, N., Lee, M. H., Gürel, M., and Ivanova, M., Self-dual codes with an automorphism of order 11, IEEE Trans. Inform. Theory, 61 (3) (2015), 1188–1193.

[Z16] Zhang, G., On the weight distributions of some cyclic codes, Discrete Math., 339 (8) (2016), 2070–2078.