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Quadratic residue codes over Galois rings
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Quadratic residue codes are cyclic codes of prime length $n$ defined over a finite field $\F_{p^e}$, where $p^e$ is a quadratic residue mod $n$. They comprise a very important family of codes. In this article we introduce the generalization of quadratic residue codes defined over Galois rings using the Galois theory.
Abstract
Quadratic residue codes are cyclic codes of prime length $n$ defined over a finite field $\F_{p^e}$, where $p^e$ is a quadratic residue mod $n$. They comprise a very important family of codes. In this article we introduce the generalization of quadratic residue codes defined over Galois rings using the Galois theory.
참고문헌 (11)
- A.R.Calderbank, "Modular and p-adic cyclic codes", Des. Codes. Cryptogr, 6, pp.21~35 (1995)
- M.H. Chiu, "Z8-cyclic codes and quadratic residue codes", Advances in Applied Math, 25, pp.12~33 (2000)
- S.T. Dougherty, "Lifted codes and their weight enumer-ators", Discrite Math, 305, pp.123~135 (2005)
- W.C. Huffman, "Fundamentals of error-correcting codes" (2003), Cambridge
- S. J. Kim, "Quadratic residue codes over Z16", Kangweon-Kyungki Math. J, 11, pp.57~64 (2003)
- S. J. Kim, "Generator polynomials of the p-adic quadratic residue codes", Kangweon-Kyungki Math. J, 13, pp.103~112 (2005)
- B. McDonald, "Finite rings with identity" (1974), Marcel Dekker
- 박영호, "Quadratic residue codes over $p$-adic integers and their projections to integers modulo $p^e$", 한국수학논문집, 23(1), pp.163~169 (2015), 강원경기수학회[DOI]
- V.S. Pless, "Cyclic codes and quadratic residue codes over Z4", IEEE Trans. Inform. Theory, 42, pp.1594~1600 (1996)
- Bijan Taeri, "Quadratic residue codes over Z9", 대한수학회지, 46(1), pp.13~30 (2009), 대한수학회
- X. Tan, "A family of quadratic residue codes over Z2m" (2011)
관련 논문AI추천
Quadratic residue codes over Z_9Bijan Taeri대한수학회 · 대한수학회지2009 · 제46권 제1호Quadratic residue codes over $p$-adic integers and their projections to integers modulo $p^e$박영호강원경기수학회 · 한국수학논문집2015 · 제23권 제1호Duadic codes over finite local ringsArezoo Soufi Karbaski, Karim Samei대한수학회 · 대한수학회보2022 · 제59권 제2호Cyclic codes over some special ringsCristina Flaut대한수학회 · 대한수학회보2013 · 제50권 제5호The $q$-adic liftings of codes over finite fields박영호강원경기수학회 · 한국수학논문집2018 · 제26권 제3호The classification of self-dual codes over Galois rings of length 4최환혁대한수학회 · 대한수학회보2018 · 제55권 제5호
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