1,120 research outputs found
Classification of extremal and -extremal binary self-dual codes of length 38
In this paper we classify all extremal and -extremal binary self-dual
codes of length 38. There are exactly 2744 extremal self-dual
codes, two -extremal codes, and 1730 -extremal
codes. We obtain our results from the use of a recursive algorithm used in the
recent classification of all extremal self-dual codes of length 36, and from a
generalization of this recursive algorithm for the shadow. The classification
of -extremal codes permits to achieve the classification of all
-extremal codes with d=6.Comment: revised version - paper submitted (4/4/2011) to IEEE trans.
Information and accepted 20/10/201
New extremal singly even self-dual codes of lengths and
For lengths and , we construct extremal singly even self-dual codes
with weight enumerators for which no extremal singly even self-dual codes were
previously known to exist. We also construct new inequivalent extremal
doubly even self-dual codes with covering radius meeting the
Delsarte bound.Comment: 13 pages. arXiv admin note: text overlap with arXiv:1706.0169
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