An Algorithm for Classification of Binary Self-Dual Codes

Abstract

An efficient algorithm for classification of binary self-dual codes is presented. As an application, a complete classification of the self-dual codes of length 38 is given.Comment: The title is change

Self-dual Rk lifts of binary self-dual codes

“…There are at least 61 R 2 self-dual (14, 2 28 , 10) codes with different weight enumerators as lifts of the [14,7,4] binary code. As the Gray images of these codes via the map φ 2 , we obtained [56, 28, 10] binary self-dual codes and by applying the extension method given in [2] by Bouyuklieva More importantly, ten new [58, 29, 10] binary self-dual codes are found. The generator matrices G i , i ∈ {1, 2, .…”

“…W 58,1 = 1 + (165 − 2β)y 10 + (5078 + 2β)y 12 + · · · (1) where 0 ≤ β ≤ 82, and W 58,2 = 1 + (319 − 24β − 2γ)y 10 + (3132 + 152β + 2γ)y 12 + · · · (2) where 0 ≤ β ≤ 11 and 0 ≤ γ ≤ 159 − 2β. New extremal self-dual codes of length 58 were obtained in [4,12,16,19,20,13].…”

“…(See[2].) If C is a binary self-dual [n = 2k + 2 > 2, k + 1, d] code then C is equivalent to a code with a generator matrix in the form 1 .…”

On the Existence of Certain Optimal Self-Dual Codes with Lengths Between 74 and 116

“…A binary self-dual code in which all weights are divisible by 4 is called a doubly even self-dual (or Type II) code, otherwise we call it a singly even self-dual (or Type I) code. All doubly even self-dual codes of length up to 40 have been classified [34], [35], [13], [2] and a classification of singly even self-dual codes of length up to 38 is also known [34], [35], [13], [4], [3], [28], [6].…”

Self-dual codes from 3-class association schemes

“…Very general versions of the building up construction of self-dual codes were given in [7] and [6]. New classification techniques have also been given in [3]. Additionally, combinatorial objects have been useful in the construction of self-dual codes.…”