Summary
2020
Session Number:B02
Session:
Number:B02-1
Finding Self-Dual Quasi-Cyclic Codes with Large Minimum Weight via Polynomial Matrices
Masaki Kawaguchi, Hajime Matsui,
pp.180-184
Publication Date:2020/10/18
Online ISSN:2188-5079
PDF download
Summary:
In this paper, we search for a class of self-dual quasi-cyclic (QC) codes over binary field with large minimum weight.We employ generator polynomial matrices to specify a QC code because there is a condition for them to be a self-dual code.
By combining factorization and Chinese remainder theorem, we efficiently search for these codes.
Moreover, under certain conditions, we use a method of reciprocal polynomials to make them more efficient.
We construct self-dual QC codes whose cycle length is 5, 7 and 9, and find them with the best minimum weight in each condition.