New extremal binary self-dual codes from F_4 + uF_4-lifts of quadratic double circulant codes over F_4

TL;DR

This paper develops new extremal binary self-dual codes of lengths 56, 58, 64, 66, and 68 using quadratic double circulant constructions over F_4 + uF_4, expanding the known catalog of such codes with new weight enumerators.

Contribution

It introduces novel extremal binary self-dual codes derived from F_4 + uF_4 lifts, with new weight enumerators, using quadratic double circulant and extension techniques.

Findings

Obtained 7 extremal codes of length 58

Generated 24 extremal codes of length 66

Created 29 extremal codes of length 68

Abstract

In this work, quadratic double and quadratic bordered double circulant constructions are applied to F_4 + uF_4 as well as F_4, as a result of which extremal binary self-dual codes of length 56 and 64 are obtained. The binary extension theorems as well as the ring extension version are used to obtain 7 extremal self-dual binary codes of length 58, 24 extremal self-dual binary codes of length 66 and 29 extremal self-dual binary codes of length 68, all with new weight enumerators, updating the list of all the known extremal self-dual codes in the literature.