논문KCI 등재
Free cyclic codes over finite local rings
0
조회
0
다운로드
2
인용
0
참고문헌
주제분류수학
초록
Abstract
In [2] it was shown that a 1-generator quasi-cyclic codeC of length n = ml of index l over Z4 is free ifC is generated bya polynomial which divides X m 1. In this paper, we prove thata necessary and sucient condition for a cyclic code over Zpk oflength m to be free is that it is generated by a polynomial whichdivides X m 1. We also show that this can be extended to nitelocal rings with a principal maximal ideal.
참고문헌 (5)
- M. F. Atiyah, "Introduction to commutative algebra" (1969), Addison-
- N. Aydin, "Quasi-cyclic codes over Z4 and some new binary codes", 48(7), pp.2065~2069 (2002)
- "Elements of Mathematics" (1972)
- P. Kanwar, "Lopez-Permouth,Cyclic codes over the integers modulo pn", 3(4), pp.334~352 (1997)
- Ling, "On the algebraic structure of cyclic code I"
관련 논문AI추천
Cyclic codes over some special ringsCristina Flaut대한수학회 · 대한수학회보2013 · 제50권 제5호Cyclic Codes of Even Length over $\mathbb Z_4$우성식대한수학회 · 대한수학회지2007 · 제44권 제3호Duadic codes over finite local ringsArezoo Soufi Karbaski, Karim Samei대한수학회 · 대한수학회보2022 · 제59권 제2호CYCLIC CODES OF LENGTH ps OVER Fpm[u] ⟨ue⟩Karim Samei, Masoumeh Mohebbei, Rashid Rezaei, Roghayeh Mohammadi Hesari대한수학회 · 대한수학회논문집2024 · 제39권 제1호On the idempotents of cyclic codes over $\mathbb{F}_{2^t}$한성휴강원경기수학회 · 한국수학논문집2022 · 제30권 제4호Quadratic residue codes over Galois rings박영호강원경기수학회 · 한국수학논문집2016 · 제24권 제3호
이 간행물의 다른 논문 (19건)
On the range closure of an elementary operatorBhagwati Prasad Duggal, Slavisa V. Djordjevi\'c, Jose Angel Canavatipp. 671-677The critical point equation on a four dimensional warped product manifold장정욱, 황승수pp. 679-692Multiplicity results for a class of second order superlinear difference systemsGuoqing Zhang, Sanyang Liupp. 693-701Jensen Type Quadratic-Quadratic Mapping in Banach Spaces박춘길, 김명중, 홍성기pp. 703-709Strong commutativity preserving mappings on semiprime ringsMuhammad Yasen, Matloob Anwar, Asif Alipp. 711-713