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- Title
LINEAR COMPLEXITY OF CYCLOTOMIC SEQUENCES OF ORDER SIX AND BCH CODES OVER GF (3).
- Authors
LIQIN HU; QIN YUE; FENGMEI LIU
- Abstract
In this paper, we always assume that p = 6f +1 is a prime. First, we calculate the values of exponential sums of cyclotomic classes of orders 3 and 6 over an extension field of GF(3). Then, we give a formula to compute the linear complexity of all pn+1-periodic generalized cyclotomic sequences of order 6 over GF(3). After that, we compute the linear complexity and the minimal polynomial of a pn+1-periodic, balanced and generalized cyclotomic sequence of order 6 over GF(3), which is analogous to a generalized Sidelnikov's sequence. At last, we give some BCH codes with prime length p from cyclotomic sequences of orders three and six.
- Subjects
LINEAR complexes; CYCLOTOMIC fields; BCH codes; FIELD extensions (Mathematics); FINITE fields; CYCLIC codes
- Publication
Advances in Mathematics of Communications, 2014, Vol 8, Issue 3, p297
- ISSN
1930-5346
- Publication type
Article
- DOI
10.3934/amc.2014.8.297