New Upper Bounds on Binary Linear Codes and a Z4 -Code With a Better-Than-Linear Gray Image

摘要

Using integer linear programming and table-lookups, we prove that there is no binary linear [1988, 12, 992] code. As a by-product, the non-existence of binary linear codes with the parameters [324, 10, 160], [356, 10, 176], [772, 11, 384], and [836, 11, 416] is shown. Our work is motivated by the recent construction of the extended dualized Kerdock code K^∗6 , which is a Z4 -linear code having a non-linear binary Gray image with the parameters (1988,212,992) . By our result, the code K^∗6 can be added to the small list of Z4 -codes for which it is known that the Gray image is better than any binary linear code.