Abstract
Let p = ef + 1 be an odd prime with positive integers e and f. In this paper, we calculate the values of Gauss periods of order e = 3, 4, 6 over a finite field GF(q), where q is a prime with q≠p. As applications, several cyclotomic sequences of order e = 3, 4, 6 are employed to construct a number of classes of cyclic codes over GF(q) with prime length. Under certain conditions, the linear complexity and reciprocal minimal polynomials of cyclotomic sequences are calculated, and the lower bounds on the minimum distances of these cyclic codes are obtained.
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Supported by the National Natural Science Foundation (NNSF) of China (No. 11171150), Foundation of Science and Technology on Information Assurance Laboratory (No. KJ-13-001), Funding of Jiangsu Innovation Program for Graduate Education (CXLX13-127, Fundamental Research Funds for the Central Universities), and Funding for Outstanding Doctoral Dissertation in NUAA (BCXJ-13-17).
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Hu, L., Yue, Q. & Zhu, X. Gauss periods and cyclic codes from cyclotomic sequences of small orders. J. Electron.(China) 31, 537–546 (2014). https://doi.org/10.1007/s11767-014-4141-3
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DOI: https://doi.org/10.1007/s11767-014-4141-3