Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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CYCLIC CODES FROM THE FIRST CLASS TWO-PRIME WHITEMAN'S GENERALIZED CYCLOTOMIC SEQUENCE WITH ORDER 6

  • Kewat, Pramod Kumar (Department of Applied Mathematics Indian Institute of Technology (Indian School of Mines)) ;
  • Kumari, Priti (Department of Applied Mathematics Indian Institute of Technology (Indian School of Mines))
  • Received : 2017.07.06
  • Accepted : 2018.09.10
  • Published : 2019.03.31
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Abstract

Let $p_1$ and $p_2$ be two distinct odd primes with gcd($p_1-1$, $p_2-1$) = 6. In this paper, we compute the linear complexity of the first class two-prime Whiteman's generalized cyclotomic sequence (WGCS-I) of order d = 6. Our results show that their linear complexity is quite good. So, the sequence can be used in many domains such as cryptography and coding theory. This article enrich a method to construct several classes of cyclic codes over GF(q) with length $n=p_1p_2$ using the two-prime WGCS-I of order 6. We also obtain the lower bounds on the minimum distance of these cyclic codes.

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References

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