Abstract

Goldberg constructed an MDS code over F9 whose ternaryimage is the ternaryGolay[12; 6; 6] code. Motivated bythe work, in this paper, we found all such MDS codes over F9 under some equivalence.

1. Introduction

An [n; k] code C over Fq is a k-dimensional vector subspace of Fn q, where Fq is the :nite :eld of order q and q is a prime power. The elements of C are called codewords. The Hamming weight wtH(x) of a codeword x is the number of non-zero coordinates in x. The dual code C⊥ of C is de:ned as C⊥ = {x ∈ Fn q | x · y = 0 for all y ∈ C}, where x · y denotes the usual inner-product.