The weight enumerators of singly-even self-dual [88,44,14] codes and new binary self-dual [68,34,12] and [88,44,14] codes

Abstract

In this work, we focus on constructing binary self-dual [68,34,12] and [88,44,14] codes with new parameters in their weight enumerators. For this purpose, we present a new bordered matrix construction for self-dual codes which is derived as a modification of two known bordered matrix constructions. We provide the necessary conditions for the new construction to produce self-dual codes over finite commutative Frobenius rings of characteristic 2. We also construct the possible weight enumerators for singly-even self-dual [88,44,14] codes and their shadows as this has not been done in the literature yet. We employ the modified bordered matrix together with the well-known neighbour method to construct binary self-dual codes that could not be obtained from the other, known bordered matrix constructions. Many of the codes turn out to have parameters in their weight enumerators that were not known in the literature before.