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Duadic codes over finite local rings
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In this paper, we introduce duadic codes over finite local rings and concentrate on quadratic residue codes. We study their properties and give the comprehensive method for the computing the unique idempotent generator of quadratic residue codes.
Abstract
In this paper, we introduce duadic codes over finite local rings and concentrate on quadratic residue codes. We study their properties and give the comprehensive method for the computing the unique idempotent generator of quadratic residue codes.
참고문헌 (8)
- M. H. Chiu, "Z8-cyclic codes and quadratic residue codes", Adv. Math. Commun, 11(1), pp.99~114 (2017)
- W. C. Huffman and V. Pless, Fundamentals of error-correcting codes, Cambridge Uni"versity Press, Cambridge, "Fundamentals of error-correcting codes" (2003), Cambridge University Press
- J. S. Leon, "Duadic codes", IEEE Trans. Inform. Theory, 30(5), pp.709~714 (1984)[DOI]
- B. R. McDonald, "Finite rings with identity, Pure and Applied Mathematics, Vol. 28" (1974), Marcel Dekker, Inc
- Graham H. Norton, "On the Structure of Linear and Cyclic Codes over a Finite Chain Ring", Applicable Algebra in Engineering, Communication and Computing, 10(6), pp.489~506 (2000), Springer Science and Business Media LLC[DOI]
- V.S. Pless, "Cyclic codes and quadratic residue codes over Z", sub 4, IEEE Transactions on Information Theory, pp.1996, 42(5)[DOI]
- R. Y. Sharp, "Steps in Commutative Algebra" (2000), Cambridge University Press
- Bijan Taeri, "Quadratic residue codes over Z_9", 대한수학회지, 46(1), pp.13~30 (2009), 대한수학회
관련 논문AI추천
Quadratic residue codes over $p$-adic integers and their projections to integers modulo $p^e$박영호강원경기수학회 · 한국수학논문집2015 · 제23권 제1호Quadratic residue codes over Galois rings박영호강원경기수학회 · 한국수학논문집2016 · 제24권 제3호Quadratic residue codes over Z_9Bijan Taeri대한수학회 · 대한수학회지2009 · 제46권 제1호Cyclic codes over some special ringsCristina Flaut대한수학회 · 대한수학회보2013 · 제50권 제5호The classification of self-dual codes over Galois rings of length 4최환혁대한수학회 · 대한수학회보2018 · 제55권 제5호Mass Formula of self-dual codes over Galois rings $GR(p^2,2)$최환혁강원경기수학회 · 한국수학논문집2016 · 제24권 제4호
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