Linear complexity of cyclotomic sequences of order six and BCH codes over GF(3)

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 $p^{n+1}$-periodic generalized cyclotomic sequences of order 6 over GF(3). After that, we compute the linear complexity and the minimal polynomial of a $p^{n+1}$-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.

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