1. \BBZ2\BBZ4 -Additive Cyclic Codes.
- Author
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Abualrub, Taher, Siap, Irfan, and Aydin, Nuh
- Subjects
- *
CYCLIC codes , *ORDERED algebraic structures , *RING theory , *POLYNOMIALS , *LINEAR codes , *BINARY codes - Abstract
In this paper, we study \BBZ2\BBZ4-additive cyclic codes. These codes are identified as \BBZ4[x]-submodules of the ring Rr,s=\BBZ2[x]/\langle x^{r}-1\rangle\times\BBZ4\left[x\right]/\langle x^{s}-1\rangle. The algebraic structure of this family of codes is studied and a set of generator polynomials for this family as a \BBZ4[x]-submodule of the ring Rr,s is determined. We show that the duals of \BBZ2\BBZ4-additive cyclic codes are also cyclic. We also present an infinite family of Maximum Distance separable with respect to the singleton bound codes. Finally, we obtain a number of binary linear codes with optimal parameters from the \BBZ2\BBZ4-additive cyclic codes. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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