论文信息 - Graph theoretic aspects of minimum distance and equivalence of binary linear codes

Graph theoretic aspects of minimum distance and equivalence of binary linear codes

A binary linear [2n, n]-code with generator matrix [In|A] can be associated with a digraph on n vertices with adjacency matrix A and vice versa. We use this connection to present a graph theoretic formula for the minimum distance of codes with information rate 1/2. We also formulate the equivalence of such codes via new transformations on corresponding digraphs.

Bahattin Yildiz | Sudipta Mallik

[1] Bernardo Gabriel Rodrigues,et al. Ternary codes from the strongly regular (45, 12, 3, 3) graphs and orbit matrices of 2-(45, 12, 3) designs , 2012, Discret. Math..

[2] Alexander Vardy,et al. The intractability of computing the minimum distance of a code , 1997, IEEE Trans. Inf. Theory.

[3] Bernardo Gabriel Rodrigues,et al. Self-orthogonal codes from the strongly regular graphs on up to 40 vertices , 2016, Adv. Math. Commun..

[4] Binary codes from the complements of the triangular graphs , 2010 .

[5] Erez Petrank,et al. Is code equivalence easy to decide? , 1997, IEEE Trans. Inf. Theory.

[6] Dimitris E. Simos,et al. The Hardness of Code Equivalence over F q and its Application to Code-based Cryptography , 2013 .

[7] Bernardo Gabriel Rodrigues,et al. LCD codes from adjacency matrices of graphs , 2018, Applicable Algebra in Engineering, Communication and Computing.

[8] Sudipta Mallik. A New Formula for the Minimum Distance of an Expander Code , 2021, ArXiv.

[9] Peter Dankelmann,et al. A Characterization of Graphs by Codes from their Incidence Matrices , 2013, Electron. J. Comb..

[10] Bahattin Yildiz,et al. Isodual and self-dual codes from graphs , 2021, Algebra and Discrete Mathematics.