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Some restrictions on weight enumerators of singly even self-dual codes II
In this note, we give some restrictions on the number of vectors of weight
in the shadow of a singly even self-dual code. This
eliminates some of the possible weight enumerators of singly even self-dual
codes for , , , and
.Comment: 16 page
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
Self-Dual Codes
Self-dual codes are important because many of the best codes known are of
this type and they have a rich mathematical theory. Topics covered in this
survey include codes over F_2, F_3, F_4, F_q, Z_4, Z_m, shadow codes, weight
enumerators, Gleason-Pierce theorem, invariant theory, Gleason theorems,
bounds, mass formulae, enumeration, extremal codes, open problems. There is a
comprehensive bibliography.Comment: 136 page
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