Abstract
The rank of a cyclic code of length \(n=2^k\) over \({\mathbb {Z}}_8\) is \(n-v\) where v is the degree of a minimal degree polynomial in the code. In this paper, minimal degree polynomials in a cyclic code C of length \(n = 2^k\) (where k is a natural number) over \({\mathbb {Z}}_8\) are determined. Further, using these minimal degree polynomials, all 95 (46 principally generated and 49 non principally generated) cyclic codes of length 4 over \({\mathbb {Z}}_8\) are calculated in terms of their distinguished sets of generators.
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Garg, A., Dutt, S. (2018). Determining Minimal Degree Polynomials of a Cyclic Code of Length \(2^k\) over \(\mathbb {Z}_8\) . In: Panda, B., Goswami, P. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2018. Lecture Notes in Computer Science(), vol 10743. Springer, Cham. https://doi.org/10.1007/978-3-319-74180-2_10
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DOI: https://doi.org/10.1007/978-3-319-74180-2_10
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