Topic
Binary cyclic group
About: Binary cyclic group is a research topic. Over the lifetime, 2 publications have been published within this topic receiving 12 citations.
Papers
17 Jan 1993
TL;DR: New cyclic group codes of length 2/sup m/ -1 over (m - j)-bit symbols are introduced and may be systematically encoded and decoded algebraically.
Abstract: New cyclic group codes of length 2/sup m/ -1 over (m - j)-bit symbols are introduced. These codes may be systematically encoded and decoded algebraically. The code rates are very close to RS codes and are much better than BCH codes (a former alternative). The (m - j )-binary tuples are identified with a sub-group of the binary m-tuples which represent the field GF(2/sup m/). Encoding is systematic and involves a two stage procedure, the usual linear feedback register (using the division or check polynomial), and a small table look up. For low rates, a second shift register encoding operation may be invoked. Decoding uses the Reed-Solomon error correcting procedures for the m-tuple alphabet, i.e., the field elements GF(2/sup m/).
12 citations
2 Jun 2016
TL;DR: The existence of an idempotent generator for group codes or group ring codes in FqG plays a very important role in determining the minimal distance of the respective code as discussed by the authors.
Abstract: The existence of an idempotent generator for group codes or group ring codes in FqG plays a very important role in determining the minimal distance of the respective code. Some necessary and sufficient conditions for a group ring element to be an idempotent in F2Cn are investigated in this paper. The main result in this paper is the affirmation of the existence of finitely many basis idempotents which gives a full identification of all idempotents in every binary cyclic group ring F2Cn. All the basis idempotents in F2Cn are able to be found by partitioning the largest idempotent’s support.
5 citations
Performance Metrics
| Year | Papers |
|---|---|
| 2016 | 1 |
| 1993 | 1 |