Abstract
There are various metrics for researching error-correcting codes. Especially, high-density data storage system gives the existence of inconsistency for the reading and writing process. The symbol-pair metric is motivated for outputs that have overlapping pairs of symbols in a certain channel. The Rosenbloom–Tsfasman (RT) metric is introduced since there exists a problem that is related to transmission over several parallel communication channels with some channels not available for the transmission. In this paper, we determine the minimum symbol-pair weight and RT weight of repeated-root cyclic codes over R=Fpm[u]/⟨u4⟩ of length n=pk. For the determination, we explicitly present third torsional degree for all different types of cyclic codes over R of length n.
Original language | English |
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Pages (from-to) | 573-588 |
Number of pages | 16 |
Journal | Applicable Algebra in Engineering, Communications and Computing |
Volume | 35 |
Issue number | 4 |
DOIs | |
State | Published - Jul 2024 |
Keywords
- Cyclic code
- Primary 94B15
- RT weight
- Secondary 94B05
- Symbol-pair weight
- Torsional degree