Cyclotomic Constructions of Cyclic Codes with Length Being the Product of Two Primes

2011/11/13 by Cunsheng Ding, Ding, Cunsheng · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1111.2991

openalex publication_date 2011/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made. In this paper, three types of generalized cyclotomy of order two and three classes of cyclic codes of length n₁n₂ and dimension (n₁n₂+1)/2 are presented and analysed, where n₁ and n₂ are two distinct primes. Bounds on their minimum odd-like weight are also proved. The three constructions produce the best cyclic codes in certain cases.

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