Wozencraft ensemble code[1]
Description
A code that is part of the Wozencraft ensemble, a set of codes most of whose members achieve the GV bound.
Each \([2k,k]_q\) code is defined by a parameter \(\alpha \in GF(q^k)\) and consists of codewords \((x,\alpha x)\) for each message \(x \in GF(q^k)\), where each element of \(GF(q^k)\) is expressed over \(GF(q)^k\) using a fixed basis.
Protection
Bounds and constructions with \(\Omega(\sqrt{k})\) distance are provided in Ref. [2].
Rate
Meets the GV bound for most choices of \(\alpha\). Puncturing the code yields a higher rate with also meeting the GV bound; see Ref. [2]. These codes can be used to asymptotically improve over the GV bound [3].
Parent
Cousin
- Justesen code — Wozencraft ensemble forms the inner codes of Justesen codes.
References
- [1]
- J. L. Massey, Threshold Decoding. Cambridge, MA: M.I.T. Press, 1963.
- [2]
- V. Guruswami and S. Li, “A Deterministic Construction of a Large Distance Code from the Wozencraft Ensemble”, (2023) arXiv:2305.02484
- [3]
- P. Gaborit and G. Zemor, “Asymptotic Improvement of the Gilbert–Varshamov Bound for Linear Codes”, IEEE Transactions on Information Theory 54, 3865 (2008) arXiv:0708.4164 DOI
Page edit log
- Victor V. Albert (2022-04-22) — most recent
Cite as:
“Wozencraft ensemble code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/wozencraft