New upper bounds on binary linear codes and a ℤ4-code with a better-than-linear Gray image
نویسندگان
چکیده
Using integer linear programming and table-lookups we prove that there is no binary linear [1988, 12, 992] code. As a byproduct, the non-existence of binary linear [324, 10, 160], [356, 10, 176], [772, 11, 384], and [836, 11, 416] codes is shown. On the other hand, there exists a linear (994, 4, 992) code over Z4. Its Gray image is a binary non-linear (1988, 2, 992) code. Therefore, we can add one more code to the small list of Z4-codes for which it is known that the Gray image is better than any binary linear code. Index Terms Linear codes, ring-linear codes, integer linear programming.
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عنوان ژورنال:
- IEEE Trans. Information Theory
دوره 62 شماره
صفحات -
تاریخ انتشار 2016