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Let $p_1$ and $p_2$ be two distinct odd primes with $\mathrm{gcd}(p_1-1,p_2-1)=6$. 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 $\mathrm{GF}(q)$ 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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참고문헌 (12)
참고문헌 신청
E. Betti / 2006 / A new bound for the minimum distance of a cyclic code from its defining set / IEEE Trans. Inform. Theory 52(8):3700~3706
Z.-X. Chen / 2008 / Some notes on generalized cyclotomic sequences of length pq / J. Comput. Sci. Tech 23(5):843~850
T. W. Cusick / 1998 / Stream Ciphers and Number Theory / North-Holland Publishing Co.
C. Ding / 1997 / Linear complexity of generalized cyclotomic binary sequences of order 2 / Finite Fields Appl 3(2):159~174
C. Ding / 2012 / Cyclic codes from the two-prime sequences / IEEE Trans. Inform. Theory 58(6):3881~3891
Z.-X. Chen / 2008 / Some notes on generalized cyclotomic sequences of length pq / J. Comput. Sci. Tech 23(5):843~850
T. W. Cusick / 1998 / Stream Ciphers and Number Theory / North-Holland Publishing Co.
C. Ding / 1997 / Linear complexity of generalized cyclotomic binary sequences of order 2 / Finite Fields Appl 3(2):159~174
C. Ding / 2012 / Cyclic codes from the two-prime sequences / IEEE Trans. Inform. Theory 58(6):3881~3891
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