On the performance of optimal double circulant even codes

TL;DR

This paper analyzes the decoding performance of optimal double circulant even codes, classifying those with minimal weight distributions up to length 72, and explores restrictions on self-dual codes with shadows, also examining extremal codes at lengths 88 and 112.

Contribution

It classifies non-self-dual optimal double circulant even codes with minimal weight distributions up to length 72 and investigates weight enumerator restrictions for certain self-dual codes.

Findings

Classified optimal double circulant even codes up to length 72.

Identified restrictions on weight enumerators of self-dual codes with shadows.

Analyzed performance of extremal self-dual codes at lengths 88 and 112.

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 $112$.