An Equivalence Based Classification of [6, 3, 4] Error Correcting Codes over GF(5)

We were able to classify all 1-error correcting [5, 3] codes over GF(5) in paper [1] and [5, 2] ternary codes in paper [2]. Now, our focus is an equivalence based classification of error correcting linear codes of length 6 over GF(5). In paper [3], we investigated the equivalence of [6,3,4] codes of length 6 and dimension 3 over GF(4). In this paper we classify the [6,3,4] codes over GF(5). We explore the weight distribution of these codes as well as their duals.