1,136 research outputs found

    New extremal singly even self-dual codes of lengths 6464 and 6666

    Get PDF
    For lengths 6464 and 6666, 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 4040 inequivalent extremal doubly even self-dual [64,32,12][64,32,12] codes with covering radius 1212 meeting the Delsarte bound.Comment: 13 pages. arXiv admin note: text overlap with arXiv:1706.0169

    Self-Dual Codes

    Get PDF
    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
    • …
    corecore