Title :
There Is No Binary [35, 10, 13] Code
Author :
Tjhai, Cen J. ; Tomlinson, Martin ; Grassl, Markus
Author_Institution :
Sch. of Comput. & Math., Univ. of Plymouth, Plymouth, UK
Abstract :
It is shown that the generator matrix of a putative linear binary code [36, 10, 14] contains the generator matrix of a [32, 7, 14] or a [33, 8, 14] binary linear code. In a first step, all nonisomorphic [32, 7, 14] and [33, 8, 14] binary codes are enumerated. Then it is shown that none of these codes yields a [35, 10, 13] linear binary code.
Keywords :
binary codes; linear codes; matrix algebra; generator matrix; nonisomorphic binary codes; putative linear binary code; Binary codes; Error correction codes; Generators; Lead; Linear code; Signal processing; Vectors; Binary codes; block codes; linear code;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2010.2100803
