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