The formula for the largest minimal distance of binary LCD $[n,2]$ codes

TL;DR

This paper derives a formula for the maximum minimal distance of binary LCD codes with parameters [n,2], advancing the understanding of their optimal properties.

Contribution

It provides the first explicit formula for the largest minimal distance of binary LCD [n,2] codes, building on prior theoretical bounds.

Findings

Derived the formula for LCD[n,2] codes

Established bounds for minimal distances of these codes

Enhanced understanding of binary LCD code optimality

Abstract

In the 2017 paper by Dougherty, Kim, Ozkaya, Sok, and Sol\'e about the linear programming bound for LCD codes the notion $\mathrm{LCD}[n,k]$ was defined for binary LCD $[n,k]$-codes. We find the formula for $\mathrm{LCD}[n,2]$.