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Dimensions of three types of BCH codes over [formula omitted].
- Source :
-
Discrete Mathematics . Aug2017, Vol. 340 Issue 8, p1910-1927. 18p. - Publication Year :
- 2017
-
Abstract
- BCH codes have been studied for over fifty years and widely employed in consumer devices, communication systems, and data storage systems. However, the dimension of BCH codes is settled only for a very small number of cases. In this paper, we study the dimensions of BCH codes over finite fields with three types of lengths n , namely n = q m − 1 , n = ( q m − 1 ) ∕ ( q − 1 ) and n = q m + 1 . For narrow-sense primitive BCH codes with designed distance δ , we investigate their dimensions for δ in the range 1 ≤ δ ≤ q ⌈ m 2 ⌉ + 1 . For non-narrow sense primitive BCH codes, we provide two general formulas on their dimensions and give the dimensions explicitly in some cases. Furthermore, we settle the minimum distances of some primitive BCH codes. We also explore the dimensions of the BCH codes of lengths n = ( q m − 1 ) ∕ ( q − 1 ) and n = q m + 1 over finite fields. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 340
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 123012136
- Full Text :
- https://doi.org/10.1016/j.disc.2017.04.001