An association between primitive and non-primitive BCH codes using monoid rings

作者：Ansari Asma Shaheen^*; Shah Tariq

来源：EURASIP Journal on Wireless Communications and Networking, 2016, 2016(1): 38.

DOI：10.1186/s13638-016-0526-3

• BCH code
• Non-primitive BCH code
• Monoid ring
• Error correction
• Code rate

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-2. We show the existence of a non-primitive binary BCH code C-bn of length bn, corresponding to a given length n binary BCH code C-n. The value of b is investigated for which the existence of the non-primitive BCH code C-bn is assured. It is noticed that the code C-n is embedded in the code C-bn. Therefore, encoding and decoding of the codes C-n and C-bn can be done simultaneously. The data transmitted by C-n can also be transmitted by C-bn. The BCH code C-bn has better error correction capability whereas the BCH code C-n has better code rate, hence both gains can be achieved at the same time.

• 出版日期2016-2-4