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

Sudipta Mallik; Bahattin Yildiz

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

Sudipta Mallik, Bahattin Yildiz

Informatics, Computing, and Cyber Systems, School of

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A binary linear [2n, n]-code with generator matrix [I_n|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.

Original language	English (US)
Pages (from-to)	515-526
Number of pages	12
Journal	Australasian Journal of Combinatorics
Volume	79
State	Published - Feb 2021

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Cite this

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abstract = "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.",

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N2 - 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.

AB - 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.

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

Abstract

ASJC Scopus subject areas

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