Abstract :
A covering code construction is presented. Using this construction it is shown that t[52,39]=3, t[36,21]=4, t[58,32]=7, K(32,2)≤62·218, and K(62,5)≤31·237, where t[n,k] is the minimum covering radius among all binary [n,k] codes and K(n,R) is the minimum cardinality of a binary code of length n and covering radius R. Four new linear codes found by computer search are also given. These include a [23,9]5 code, a [32,8]10 code, a [51,41]2 code, and a [45,20]8 code.
Keywords :
binary codes; linear codes; set theory; ADS-like construction; amalgamated direct sum; binary codes; code length; computer search; covering codes; minimum cardinality; minimum covering radius; set theory; Binary codes; Computer science; Error correction codes; Linear code; Mathematics; Parity check codes; Vectors;
