LinCode - computer classification of linear codes

We present an algorithm for the classification of linear codes over finite fields, based on lattice point enumeration. We validate a correct implementation of our algorithm with known classification results from the literature, which we partially extend to larger ranges of parameters.

[1]  Iliya Bouyukliev.  About the code equivalence , 2007 .

[2]  Gordon F. Royle.  An orderly algorithm and some applications in finite geometry , 1998, Discret. Math..

[3]  David B. Jaffe.  Optimal binary linear codes of length leq 30 , 2000, Discret. Math..

[4]  Iliya Bouyukliev,et al.  What is Q-extension? , 2007, Serdica Journal of Computing.

[5]  D. Slepian.  Some further theory of group codes , 1960 .

[6]  Sascha Kurz,et al.  On the Lengths of Divisible Codes , 2017, IEEE Transactions on Information Theory.

[7]  H. Ward.  Divisible Codes - A Survey , 2001 .

[8]  P. Kaski,et al.  Classification Algorithms for Codes and Designs , 2005 .

[9]  Alfred Wassermann,et al.  Attacking the Market Split Problem with Lattice Point Enumeration , 2002, J. Comb. Optim..

[10]  Alfred Wassermann,et al.  Projective divisible binary codes , 2017 .

[11]  A. Kerber,et al.  Error-correcting linear codes : classification by isometry and applications , 2006 .

[12]  Alexander Barg,et al.  Minimal Vectors in Linear Codes , 1998, IEEE Trans. Inf. Theory.

[13]  Patric R. J. Östergård.  Classifying Subspaces of Hamming Spaces , 2002, Des. Codes Cryptogr..

[14]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[15]  Stefka Bouyuklieva,et al.  Classification of linear codes using canonical augmentation , 2019, ArXiv.

[16]  A. Hora,et al.  Distance-Regular Graphs , 2007 .

[17]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[18]  László Lovász,et al.  Factoring polynomials with rational coefficients , 1982 .

[19]  Stefan M. Dodunekov,et al.  Codes and Projective Multisets , 1998, Electron. J. Comb..

[20]  Alfred Wassermann,et al.  The Lengths of Projective Triply-Even Binary Codes , 2020, IEEE Transactions on Information Theory.

[21]  Thomas Feulner.  The automorphism groups of linear codes and canonical representatives of their semilinear isometry classes , 2009, Adv. Math. Commun..

[22]  Harold N. Ward,et al.  Divisible codes , 1981 .

[23]  B. McKay.  nauty User ’ s Guide ( Version 2 . 4 ) , 1990 .