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Shortened Hamming Codes Maximizing Double Error Detection

Discrete Mathematics 2011-05-24 v2 Information Theory math.IT

Abstract

Given r3r\geq 3 and 2r1+1n<2r12^{r-1}+1\leq n< 2^{r}-1, an [n,nr,3][n,n-r,3] shortened Hamming code that can detect a maximal number of double errors is constructed. The optimality of the construction is proven.

Keywords

Cite

@article{arxiv.1011.1933,
  title  = {Shortened Hamming Codes Maximizing Double Error Detection},
  author = {Mario Blaum and Sugata Sanyal},
  journal= {arXiv preprint arXiv:1011.1933},
  year   = {2011}
}

Comments

We withdraw the paper since we found a reference from 1981 that solves exactly the same problem

R2 v1 2026-06-21T16:40:50.037Z