Berlekamp code

Berlekamp code[1; Ch. 9]

Description

A linear \(p\)-ary code that has Lee distance 5 and whose construction resembles that of RS codes. It is obtained by first constructing an RS-like parity-check matrix out of a certain field extension of \(GF(p)\) and then taking the subfield subcode of the corresponding code; see [2; Ch. 10.6].

Parents

Linear \(q\)-ary code
Constacyclic code — Berlekamp codes are negacyclic [1; Ch. 9].

Cousins

Alternant code — Berlekamp codes reduce to narrow-sense alternant codes for \(p=2\) [2; Ch. 10.6].
Reed-Solomon (RS) code — Berlekamp codes are obtained by first constructing an RS-like parity-check matrix out of a certain field extension of \(GF(p)\) and then taking the subfield subcode of the corresponding code; see [2; Ch. 10.6].

References

[1]: E. R. Berlekamp, Algebraic Coding Theory (WORLD SCIENTIFIC, 2014) DOI
[2]: R. Roth, Introduction to Coding Theory (Cambridge University Press, 2006) DOI

Page edit log

Victor V. Albert (2024-08-09) — most recent

Cite as:

“Berlekamp code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/berlekamp

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/ag/reed_solomon/berlekamp.yml.