Nadler code[1]
Description
A nonlinear \((12,35,5)\) binary code that is the largest double-error-correcting code.
An inequivalent code with the same parameters was constructed by Van Lint [2] and presented in [3; Ch. 2, Sec. 8]. Its automorphism group is a subgroup of \(S_3\times S_4\) [2].
While the two codes are inequivalent, the \((13,64,5)\) extension of both codes is unique and is a shortened NR code [4].
Parent
Cousin
- Nordstrom-Robinson (NR) code — The NR code is an extension of the Nadler code [2,4].
References
- [1]
- M. Nadler, “A 32-point n=12, d=5 code (Corresp.)”, IRE Transactions on Information Theory 8, 58 (1962) DOI
- [2]
- J. van Lint, “A new description of the Nadler code (Corresp.)”, IEEE Transactions on Information Theory 18, 825 (1972) DOI
- [3]
- F. J. MacWilliams and N. J. A. Sloane. The theory of error correcting codes. Elsevier, 1977.
- [4]
- J.-M. Goethals, “The extended Nadler code is unique (Corresp.)”, IEEE Transactions on Information Theory 23, 132 (1977) DOI
Page edit log
- Victor V. Albert (2024-08-15) — most recent
Cite as:
“Nadler code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/nadler