Self-dual double cyclic codes over $\mathbb{Z}_2$

Subject Areas : Combinatorics, Graph theory

H. Movahedi ¹ (Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran)
L. Pourfaraj ² (Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran)

Received: 2021-08-23 Accepted : 2021-11-09 Published : 2021-12-14

Keywords: Canonical projections, double cyclic codes, self-dual codes, shadow codes,

Abstract :

A double cyclic code (or \emph{DC code}) of length $n=k+l$ over $\mathbb{Z}_2$ is a binary linear code, where any cyclic shift of the first $k$ coordinates and the last $l$ coordinates of a codeword is also a codeword. In this paper, we study the relationship between separability and self-duality of these codes. Also, we obtain the shadow code by determining the generator polynomials of the doubly even subcode of the self-dual code.

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