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- Title
An association between primitive and non-primitive BCH codes using monoid rings.
- Authors
Ansari, Asma; Shah, Tariq
- Abstract
BCH codes are one of the most important classes of cyclic codes for error correction. In this study, we generalize BCH codes using monoid rings instead of a polynomial ring over the binary field F. We show the existence of a non-primitive binary BCH code C of length bn, corresponding to a given length n binary BCH code C. The value of b is investigated for which the existence of the non-primitive BCH code C is assured. It is noticed that the code C is embedded in the code C. Therefore, encoding and decoding of the codes C and C can be done simultaneously. The data transmitted by C can also be transmitted by C. The BCH code C has better error correction capability whereas the BCH code C has better code rate, hence both gains can be achieved at the same time.
- Subjects
BCH codes; MONOIDS; ERROR correction (Information theory); POLYNOMIAL rings; CODING theory
- Publication
EURASIP Journal on Wireless Communications & Networking, 2016, Vol 2016, Issue 1, p1
- ISSN
1687-1472
- Publication type
Article
- DOI
10.1186/s13638-016-0526-3