منابع مشابه
An Extremal Doubly Even Self-Dual Code of Length 112
In this note, an extremal doubly even self-dual code of length 112 is constructed for the first time. This length is the smallest length for which no extremal doubly even self-dual code of length n 6≡ 0 (mod 24) has been constructed.
متن کاملDoubly-even Self-dual Code over F 4
We show that there is no [24, 12, 9] doubly-even self-dual code over F4 by attempting to construct the generator matrix of this code directly.
متن کاملOn self-dual doubly-even extremal codes
Let C be a binary linear self-dual doubly-even code of length n and minimal weight d. Such codes exist only if 12 = 0 (mod 8). We put II = 24r + 8s, s = 0, 1, 2. It follows from the work of Gleason [2] and of Mallows and Sloane [6] that d s 4r + 4. C is called extremal if d = 4r + 4. In the following, an extremal code means a binary linear self-dual doubly-even extremal code. We use the set-the...
متن کاملThe extended quadratic residue code is the only (48, 24, 12) self-dual doubly-even code
The largest minimum weight of a self-dual doubly-even binary (n, k, d) code is d = 4bn/24c+ 4. Of such codes with length divisible by 24, the Golay Code is the only (24, 12, 8) code, the Extended Quadratic Residue Code is the only known (48, 24, 12) code, and there is no known (72, 36, 16) code. One may partition the search for a (48, 24, 12) self-dual doubly-even code into 3 cases. A previous ...
متن کاملOn a 5-design related to a putative extremal doubly even self-dual code of length a multiple of 24
By the Assmus and Mattson theorem, the codewords of each nontrivial weight in an extremal doubly even self-dual code of length 24m form a self-orthogonal 5-design. In this paper, we study the codes constructed from self-orthogonal 5-designs with the same parameters as the above 5-designs. We give some parameters of a self-orthogonal 5-design whose existence is equivalent to that of an extremal ...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2002
ISSN: 0018-9448
DOI: 10.1109/18.979333