Seven new champion linear codes

TL;DR

This paper presents seven new linear codes over F_8 with improved minimum distances, discovered through exhaustive search of monomial evaluation codes on a 6x6 lattice, surpassing previous best known codes.

Contribution

The authors introduce seven new linear codes with better minimum distances than existing codes for the same parameters, using a novel exhaustive search method.

Findings

Seven new codes with higher minimum distances identified

Codes are defined over F_8 with specific [n,k,d] parameters

Exhaustive search method over a lattice square used for discovery

Abstract

We exhibit seven linear codes exceeding the current best known minimum distance d for their dimension k and block length n. Each code is defined over F_8, and their invariants [n,k,d] are given by [49,13,27], [49,14,26], [49,16,24], [49,17,23], [49,19,21], [49,25,16] and [49,26,15]. Our method includes an exhaustive search of all monomial evaluation codes generated by points in the [0,5]x[0,5] lattice square.