Korean Journal of Mathematics

  • 제27권3호
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  • Pages.767-777
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  • 2019
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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CYCLIC CODES OVER THE RING OF 4-ADIC INTEGERS OF LENGTHS 15, 17 AND 19

  • Park, Young Ho (Department of Mathematics Kangwon National University)
  • 투고 : 2019.07.23
  • 심사 : 2019.09.08
  • 발행 : 2019.09.30
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초록

We present a new way of obtaining the complete factorization of $X^n-1$ for n = 15, 17, 19 over the 4-adic ring ${\mathcal{O}}_4[X]$ of integers and thus over the Galois rings $GR(2^e,2)$. As a result, we determine all cyclic codes of lengths 15, 17 and 19 over those rings. This extends our previous work on such cyclic codes of odd lengths less than 15.

키워드

참고문헌

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