# New Binary Singly Even Self-Dual Codes

@article{Harada2010NewBS, title={New Binary Singly Even Self-Dual Codes}, author={Masaaki Harada and Michael Kiermaier and Alfred Wassermann and Radinka Yorgova}, journal={IEEE Transactions on Information Theory}, year={2010}, volume={56}, pages={1612-1617} }

In this paper, we construct new binary singly even self-dual codes with larger minimum weights than the previously known singly even self-dual codes for several lengths. Several known construction methods are used to construct the new self-dual codes.

## 15 Citations

Eighth Power Residue Double Circulant Self-Dual Codes

- Computer ScienceInt. J. Netw. Secur.
- 2020

New constructions of self-dual codes over GF(2) and GF(4) by eighth power residues are given, including multiple pure double circulant codes and bordered double circULant codes.

New binary self-dual codes of lengths 56, 62, 78, 92 and 94 from a bordered construction

- Computer Science, MathematicsArXiv
- 2021

Using a new bordered construction for self-dual codes which employs λ-circulant matrices, this paper constructs many binary self- dual codes of lengths 56, 62, 78, 92 and 94 with parameters in their weight enumerators that were not known in the literature before.

The search of Type I codes

- Computer ScienceArXiv
- 2021

The purpose of this paper is to investigate interesting properties of Type I codes of different lengths, and to build up a computer-based code-searching program based on knowledge about Type I code.

Fourth Power Residue Double Circulant Self-Dual Codes

- Computer ScienceIEEE Transactions on Information Theory
- 2015

New infinite families of self-dual codes over GF(2, GF(3), GF(4),GF(8), and GF(9) are introduced and some of them have better minimum weight than previously known codes.

Singly even self-dual codes of length 24k + 10 and minimum weight 4k + 2

- Computer ScienceCryptography and Communications
- 2018

Some restrictions on the possible weight enumerators of singly even self-dual [24k + 10, 12k + 5, 4k + 2] codes with shadows of minimum weight at least 5 for k = 2, 3, 4, 5 are given.

Double-circulant and bordered-double-circulant constructions for self-dual codes over R2

- Computer Science, MathematicsAdv. Math. Commun.
- 2012

Using these methods, three extremal binary Type I codes of length $64$ of new weight enumerators for which extremal codes were not known to exist are constructed.

Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours

- Computer ScienceAdvances in Mathematics of Communications
- 2022

This work defines a modification of a bordered construction for self-dual codes which utilises <inline-formula><tex-math id="M1">-circulant matrices and provides the necessary conditions for the construction to produce self- dual codes over finite commutative Frobenius rings of characteristic 2.

On extremal double circulant self-dual codes of lengths 90–96

- Computer Science, MathematicsApplicable Algebra in Engineering, Communication and Computing
- 2019

A classification of extremal double circulant self-dual codes of lengths up to 88 is known and this classification is extended to length 96, where it is demonstrated that no doublecirculantSelfdual [90, 45, 14] code has an extremal self- dual neighbor.

On the self-dual codes invariant under an automorphism of type 11-(8,0)

- Computer Science2020 Algebraic and Combinatorial Coding Theory (ACCT)
- 2020

It is proved that [8],[4] SD codes over F210 such that their preimage is a binary code with minimum weight 20 does not exist, and many new Hermitian self-dual codes are found, allowing us to constructed 468062 new binary SD [88,44,16] doubly-even codes.

Extremal binary self-dual codes of lengths 64 and 66 from four-circulant constructions over F2+uF2

- Computer Science
- 2014

Five codes are new codes in the sense that codes with these weight enumerators are constructed for the first time and have the values = 1; 30; 34; 84; 94 in W66;1.

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