1. Maximum distance separable codes for b-symbol read channels.
- Author
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Ding, Baokun, Zhang, Tao, and Ge, Gennian
- Subjects
- *
MATHEMATICAL sequences , *MATHEMATICAL bounds , *PROJECTIVE geometry , *FINITE fields , *EXISTENCE theorems - Abstract
Recently, Yaakobi et al. introduced codes for b -symbol read channels, where the read operation is performed as a consecutive sequence of b > 2 symbols. In this paper, we establish a Singleton-type bound for b -symbol codes. Codes meeting the Singleton-type bound are called maximum distance separable (MDS) codes, and they are optimal in the sense they attain the maximal minimum b -distance. We introduce a construction method using projective geometry, and then construct several infinite families of linear MDS b -symbol codes over finite fields. The lengths of these codes have a large range. And in some sense, we completely determine the existence of linear MDS b -symbol codes over finite fields for certain parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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