Self-Dual Codes

E.M. Rains; N.J.A. Sloane

Self-Dual Codes

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arxiv math/0208001 v1 pith:S2O4AXBN submitted 2002-08-01 math.CO cs.ITmath.IT

E.M. Rains , N.J.A. Sloane This is my paper · ORCID

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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.

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Symmetry-guided constructions of absolutely maximally entangled states in five open cases
quant-ph 2026-08 conditional novelty 7.0 of 10

New explicit Hermitian self-dual MDS codes yield AME(12,5), AME(18,11), AME(18,13), and their 17-party projections.

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