Construction for both self-dual codes and LCD codes

TL;DR

This paper introduces a method to construct new codes with identical hull dimensions, enabling the creation of self-dual and LCD codes, and improves bounds on the minimum weights of certain binary LCD codes.

Contribution

The paper presents a novel construction method for codes preserving hull dimensions, leading to new extremal codes and improved bounds on binary LCD code parameters.

Findings

Constructed 661 new extremal doubly even [56, 28, 12] codes.

Improved lower bounds on the largest minimum weights for binary LCD codes with lengths 26 to 40.

Abstract

From a given $[n, k]$ code $C$, we give a method for constructing many $[n, k]$ codes $C'$ such that the hull dimensions of $C$ and $C'$ are identical. This method can be applied to constructions of both self-dual codes and linear complementary dual codes (LCD codes for short). Using the method, we construct 661 new inequivalent extremal doubly even $[56, 28, 12]$ codes. Furthermore, constructing LCD codes by the method, we improve some of the previously known lower bounds on the largest minimum weights of binary LCD codes of length $n=26,28 \le n \le 40$.