An additive \((n,2^n)_q\) code that is equal to its dual, \(C^\perp = C\), where the dual is defined with respect to some inner product, usually the trace-Hermitian inner product.
Self-dual additive codes that contain at least one codeword of odd weight are called Type I additive. Even self-dual additive codes are called Type II additive, existing only for even \(n\) [1; Sec. 9.10]. Type I (type II) additive codes with length up to seven (eight) have been classified . Much is known about codes up to length 16 .
- Self-dual linear code — Self-dual linear codes with respect to some inner product are automatically self-dual additive under the same inner product since linear codes are additive. In addition, quaternary linear codes are Hermitian self-orthogonal (self-dual) iff they are trace-Hermitian self-orthogonal (self-dual) additive [5; Thm. 27.4.1] ([1; Thm. 9.10.3]).
- Dodecacode — The dodecacode is trace-Hermitian self-dual additive.
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- M. F. Ezerman, "Quantum Error-Control Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
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- Victor V. Albert (2022-07-22) — most recent
“Self-dual additive code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/self_dual_additive