New Upper Bounds on Binary Linear Codes and a Z(4)-Code With a Better-Than-Linear Gray Image

作者：Kiermaier Michael^*; Wassermann Alfred; Zwanzger Johannes

来源：IEEE Transactions on Information Theory, 2016, 62(12): 6768-6771.

DOI：10.1109/TIT.2016.2612654

• Linear codes
• ring-linear codes
• Kerdock codes
• integer linear programming

Using integer linear programming and tablelookups, 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) over cap (6)* 6, which is a Z(4)-linear code having a non-linear binary Gray image with the parameters (1988, 212, 992). By our result, the code (K) over cap (6)* can be added to the small list of Z(4)-codes for which it is known that the Gray image is better than any binary linear code.

• 出版日期2016-12