An analysis of Chen's construction of minimum-distance five codes
In 1991, C. L. Chen used the inverted construction Y-1 on binary linear codes of minimum Hamming distance five to construct a new [47, 36, 5] code. In this paper, we examine this construction in depth and show that no such codes are obtained unless the fields GF (8) or GF (32) are used. Using MAGMA, we prove that the binary [11, 4, 5] code and the binary [15, 7, 5] extension found by Chen are the only possible such codes using the held GF(8); indeed, the latter is a Bose-Chaudhuri-Hocquenghem (BCH) code, We prove also that, using the field GF (32), precisely three nonequivalent binary [47, 36, 5] codes arise along with one extension to a [63, 51, 5] code.
inverted construction y-1 error-correcting code minimum distance