Publication
A BCH code and a sequence of cyclic codes
| Summary: | This study establishes that for a given binary BCH code C0 n of length n generated by a polynomial g(x) ∈ F2[x] of degree r there exists a family of binary cyclic codes {Cm 2m−1(n+1)n}m≥1 such that for each m ≥ 1, the binary cyclic code Cm 2m−1(n+1)n has length 2m−1(n + 1)n and is generated by a generalized polynomial g(x 1 2m ) ∈ F2[x, 1 2m Z≥0] of degree 2mr. Furthermore, C0 n is embedded in Cm 2m−1(n+1)n and Cm 2m−1(n+1)n is embedded in Cm+1 2m(n+1)n for each m ≥ 1. By a newly proposed algorithm, codewords of the binary BCH code C0 n can be transmitted with high code rate and decoded by the decoder of any member of the family {Cm 2m−1(n+1)n}m≥1 of binary cyclic codes, having the same code rate. |
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| Main Authors: | Andrade, Antonio Aparecido de |
| Other Authors: | Shah, Tariq; Khan, Mubashar |
| Subject: | Cyclic code BCH code decoding procedure |
| Year: | 2015 |
| Country: | Brazil |
| Document type: | article |
| Access type: | open access |
| Associated institution: | IBICT |
| Language: | English |
| Origin: | Oasisbr |
| Summary: | This study establishes that for a given binary BCH code C0 n of length n generated by a polynomial g(x) ∈ F2[x] of degree r there exists a family of binary cyclic codes {Cm 2m−1(n+1)n}m≥1 such that for each m ≥ 1, the binary cyclic code Cm 2m−1(n+1)n has length 2m−1(n + 1)n and is generated by a generalized polynomial g(x 1 2m ) ∈ F2[x, 1 2m Z≥0] of degree 2mr. Furthermore, C0 n is embedded in Cm 2m−1(n+1)n and Cm 2m−1(n+1)n is embedded in Cm+1 2m(n+1)n for each m ≥ 1. By a newly proposed algorithm, codewords of the binary BCH code C0 n can be transmitted with high code rate and decoded by the decoder of any member of the family {Cm 2m−1(n+1)n}m≥1 of binary cyclic codes, having the same code rate. |
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