An unrestricted q-ary maximum distance separable (MDS) code C with length n over an alphabet A (of size q) is a set of qk codewords that are elements of An, such that the smallest Hamming distance between two distinct codewords in C is d = n ̶ k + 1. Sets of mutually orthogonal Latin squares of orders q ≤ 9, corresponding to q-ary MDS codes of size q2, and q-ary one-error-correcting MDS codes for q ≤ 8 have been classified in earlier studies. These results are used here to complete the classification of all 7-ary and 8-ary MDS codes with d ≥ 3 using a computer search.
|Number of pages||10|
|Journal||Advances in Mathematics of Communications|
|Publication status||Published - 1 Aug 2016|
|MoE publication type||A1 Journal article-refereed|
- Latin hypercube
- MDS code