On the Minimum Redundancy of SEC-DAEC-TAEC Binary Linear Block Codes

The redundancy n - k of an (n, k) binary linear block code capable of single error correction, double adjacent error correction and triple adjacent error correction (SEC-DAECTAEC) is lower bounded by log
₂
(3n - 2). Recently, researchers have tried to find minimum redundancy codes which achieve equality in this lower bound using computer search and failed. In this letter, we prove that such codes do not exist for any n and k. This results in the tighter lower bound of n - k ≥ log
₂
(3n - 1) on the redundancy of SEC-DAEC-TAEC codes.