Seven new champion linear codes
Gavin Brown, Alexander M. Kasprzyk

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
