Name
Abstract | ||
|---|---|---|
BCH codes are among the best practical cyclic codes widely used in consumer electronics, communication systems, and storage devices. However, not much is known about BCH codes with large minimum distance. In this paper, we consider narrow-sense BCH codes of length n = q(m)-1/N with designed distance delta = s q-1/n proportional to n, where N divides qm-1/q-1 and 1 \leq s \leq q 1. We determine both their dimensions and minimum distances. In particular, when N = 1, the codes are primitive, with minimum distance d = s/q-1n (qm 1) and dimension k = (q s)m. The general result on code dimensions is achieved by applying generating functions and inverse discrete Fourier transforms to an enumeration problem. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1137/19M1260876 | SIAM JOURNAL ON DISCRETE MATHEMATICS |
Keywords | DocType | Volume |
BCH code, minimum distance, dimension, cyclotomic coset, generating function, inverse discrete Fourier transform | Journal | 35 |
Issue | ISSN | Citations |
1 | 0895-4801 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Satoshi Noguchi | 1 | 0 | 0.34 |
| Xiaonan Lu | 2 | 4 | 3.12 |
| Masakazu Jimbo | 3 | 177 | 30.81 |
| Ying Miao | 4 | 491 | 43.85 |