An analysis of Chen´s construction of minimum-distance five codes

In 1991, C.L. Chen used the inverted construction Y₁ on binary linear codes of minimum Hamming distance five to construct a new [47, 36, 5] code. 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 field 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