Author:
Brown Gavin,Kasprzyk Alexander M.
Abstract
AbstractWe 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 ${ \mathbb{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] \times [0, 5] $ lattice square.
Subject
Computational Theory and Mathematics,General Mathematics
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