Binary linear complementary dual codes

TL;DR

This paper investigates binary linear complementary dual codes, focusing on their maximum minimum weight and providing classifications for small dimensions and lengths up to 16.

Contribution

It characterizes and classifies binary linear complementary dual codes with the largest minimum weight for small parameters and provides a complete classification for lengths up to 16.

Findings

Identified maximum minimum weights for small-dimensional codes.

Provided classifications for codes with length up to 16.

Characterized codes with the largest minimum weight for small dimensions.

Abstract

Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study binary linear complementary dual $[n,k]$ codes with the largest minimum weight among all binary linear complementary dual $[n,k]$ codes. We characterize binary linear complementary dual codes with the largest minimum weight for small dimensions. A complete classification of binary linear complementary dual $[n,k]$ codes with the largest minimum weight is also given for $1 \le k \le n \le 16$.