New binary self-dual codes of lengths 56, 58, 64, 80 and 92 from a modification of the four circulant construction

Abstract

In this work, we give a new technique for constructing self-dual codes over commutative Frobenius rings using $\lambda$-circulant matrices. The new construction was derived as a modification of the well-known four circulant construction of self-dual codes. Applying this technique together with the building-up construction, we construct singly-even binary self-dual codes of lengths 56, 58, 64, 80 and 92 that were not known in the literature before. Singly-even self-dual codes of length 80 with $\beta \in \{2,4,5,6,8\}$ in their weight enumerators are constructed for the first time in the literature.

arXiv commentcorrected typos; added references

References in corpus (3)

• New extremal singly even self-dual codes of lengths $64$ and $66$
• Binary extremal self-dual codes of length $60$ and related codes
• A group induced four-circulant construction for self-dual codes and new extremal binary self-dual codes

Cited by in corpus (4)

• Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours
• New binary self-dual codes of lengths 56, 62, 78, 92 and 94 from a bordered construction
• Quaternary Hermitian self-dual codes of lengths 26, 32, 36, 38 and 40 from modifications of well-known circulant constructions
• New binary self-dual codes of lengths 80, 84 and 96 from composite matrices