New upper bounds on binary linear codes and a ℤ₄-code with a better-than-linear Gray image

Titelangaben

Kiermaier, Michael ; Wassermann, Alfred ; Zwanzger, Johannes:
New upper bounds on binary linear codes and a ℤ₄-code with a better-than-linear Gray image.
In: IEEE Transactions on Information Theory. Bd. 62 (2016) Heft 12 . - S. 6768-6771.
ISSN 0018-9448
DOI: https://doi.org/10.1109/TIT.2016.2612654

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Abstract

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 K6*, which is a Z4-linear code having a non-linear binary Gray image with the parameters 1988, 212,992. By our result, the code K6* 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.