New Construction of A Family of Quasi-Twisted Two-Weight Codes

Abstract

Based on cyclic and consta-cyclic simplex codes, a new explicit construction of a family of two-weight codes is presented. These two-weight codes obtained are in the form of 2-generator quasi-cyclic, or quasi-twisted structure. Based on this construction, new optimal binary quasi-cyclic [195, 8, 96], [210, 8, 104] and [240, 8, 120] codes, and good QC ternary [208, 6, 135] and [221, 6, 144] codes are thus obtained. It is also shown that many codes among the family meet the Griesmer bound and thereful are optimal.

arXiv comment4 pages, submitted to IEEE Trans. Information Theory