Ideal structure of Zq + uZq and Zq + uZq-cyclic codes
Keyword(s):
Gray Map
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In this paper, we study cyclic codes of length n over R = Zq + uZq, u2 = 0, where q is a power of a prime p and (n; p) = 1. We have determined the complete ideal structure of R. Using this, we have obtained the structure of cyclic codes and that of their duals through the factorization of xn-1 over R. We have also computed total number of cyclic codes of length n over R. A necessary and sufficient condition for a cyclic code over R to be self-dual is presented. We have presented a formula for the total number of self-dual cyclic codes of length n over R. A new Gray map from R to Z2rp is defined. Using Magma, some good cyclic codes of length 4 over Z9 + uZ9 are obtained.
2016 ◽
Vol 08
(01)
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pp. 1650017
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Keyword(s):
2015 ◽
Vol 13
(03)
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pp. 1550031
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2016 ◽
Vol 14
(01)
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pp. 1650012
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2018 ◽
Vol 10
(03)
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pp. 1850033
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2019 ◽
Vol 18
(04)
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pp. 1950077
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2015 ◽
Vol 07
(04)
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pp. 1550058
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2018 ◽
Vol 11
(06)
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pp. 1850078
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2017 ◽
Vol E100.A
(12)
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pp. 2764-2775
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