Optimal $q$ -Ary Error Correcting/All Unidirectional Error Detecting Codes

Codes that can correct up to t symmetric errors and detect all unidirectional errors, known as t-EC-AUED codes, are studied in this paper. Given positive integers q, a, and t, let n
_q
(a, t + 1) denote the length of the shortest q-ary t-EC-AUED code of size a. We introduce combinatorial constructions for q-ary t-EC-AUED codes via one-factorizations of complete graphs, and concatenation of MDS codes and codes from resolvable set systems. Consequently, we determine the exact values of n
_q
(a, t + 1) for several new infinite families of q, a, and t.