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http://dx.doi.org/10.11568/kjm.2022.30.4.653

ON THE IDEMPOTENTS OF CYCLIC CODES OVER 𝔽2t  

Sunghyu, Han (School of Liberal Arts, KoreaTech)
Publication Information
Korean Journal of Mathematics / v.30, no.4, 2022 , pp. 653-663 More about this Journal
Abstract
We study cyclic codes of length n over 𝔽2t. Cyclic codes can be viewed as ideals in 𝓡n = 𝔽2t [x]/(xn − 1). It is known that there is a unique generating idempotent for each ideal. Let e(x) ∈ 𝓡n. If t = 1 or t = 2, then there is a necessary and sufficient condition that e(x) is an idempotent. But there is no known similar result for t ≥ 3. In this paper we give an answer for this problem.
Keywords
cyclic codes; finite fields; idempotents;
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  • Reference
1 W. C. Huffman, V. S. Pless, Fundamentals of Error-correcting Codes, Cambridge: Cambridge University Press, 2003.
2 W. W. Peterson, Error-Correcting Codes, Cambridge, MA: MIT Press, 1961.
3 W. W. Peterson, E. J. Weldon, Jr., Error-Correcting Codes, 2nd ed. Cambridge, MA.: MIT Press, 1972.