One-error correcting [5, 2] ternary codes

Abstract

In this paper, using equivalence, we classify the error correcting linear codes of length 5 and dimension 2 over GF(3). We are able to show that these codes can be partitioned into 3 mutually disjoint equivalence classes. In the final section, we compute the weight distributions of the of the codes belonging to various distinct classes. We did similar investigations for [5,2] codes over GF(4) in [1].

Subject Classification:

• (2010) 11T71

Keywords:

• Linear code
• Equivalent code
• Codeword
• Minimum weight