Generator polynomials and generator matrix for quasi cyclic codes

2017/04/28 by Zahra Sepasdar, Sepasdar, Zahra
Computer Science · Medicine · #Cancer Mechanisms and Therapy #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.1704.08815

openalex publication_date 2017/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Quasi-cyclic (QC) codes form an important generalization of cyclic codes. It is well know that QC codes of length sℓ with index s over the finite field \mathbbF are \mathbbF[y]-submodules of the ring \frac\mathbbF[x,y]< x^s-1,y^ℓ-1 >. The aim of the present paper, is to study QC codes of length sℓ with index s over the finite field \mathbbF and find generator polynomials and generator matrix for these codes. To achieve this aim, we apply a novel method to find generator polynomials for \mathbbF[y]-submodules of \frac\mathbbF[x,y]< x^s-1,y^ℓ-1 >. These polynomials will be applied to obtain generator matrix for corresponding QC codes.

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