Description
Cyclic \([2^m -1, 2^m - 1 - 2m, 5]\) linear code with generator polynomial is \(g(x) = p(x)p(x)^{\star}\), where \(p(x)\) is a primitive polynomial of degree \(m\) that is the minimal polynomial over \(GF(2)\) of an element \(\alpha\) of order \(2^m -1\) in \(GF(2^m)\), \(m\) is odd and greater that five, and '\(\star\)' denotes reciprocation [3].
Decoding
Algebraic decoder [3].
Parents
Cousin
- Quaternary linear code over \(\mathbb{Z}_4\) — The even-weight subcode of the Melas code can be lifted to a code over \(\mathbb{Z}_4\) [3].
References
- [1]
- C. M. Melas, “A Cyclic Code for Double Error Correction [Letter to the Editor]”, IBM Journal of Research and Development 4, 364 (1960) DOI
- [2]
- G. van der Geer and M. van der Vlugt, “Generalized Hamming Weights of Melas Codes and Dual Melas Codes”, SIAM Journal on Discrete Mathematics 7, 554 (1994) DOI
- [3]
- A. Alahmadi, H. Alhazmi, T. Helleseth, R. Hijazi, N. Muthana, and P. Solé, “On the lifted Melas code”, Cryptography and Communications 8, 7 (2015) DOI
Page edit log
- Victor V. Albert (2022-01-02) — most recent
- Khalil Guy (2022-01-02)
Cite as:
“Melas code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/melas
Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/cyclic/melas.yml.