On the performance of optimal double circulant even codes

2016/04/23 by T. Aaron Gulliver, Gulliver, T. Aaron, Masaaki Harada +1
Computer Science · Engineering · Mathematics · #94B05 #94B70 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1604.06878

openalex publication_date 2016/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we investigate the performance of optimal double circulant even codes which are not self-dual, as measured by the decoding error probability in bounded distance decoding. To do this, we classify the optimal double circulant even codes that are not self-dual which have the smallest weight distribution for lengths up to 72. We also give some restrictions on the weight enumerators of (extremal) self-dual [54,27,10] codes with shadows of minimum weight 3. Finally, we consider the performance of extremal self-dual codes of lengths 88 and 112.

Citations

• A new upper bound on the minimal distance of self-dual codes

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