Trace Representation over F_r of Binary Jacobi Sequences with Period pq

抄録

In this letter, we give a trace representation of binary Jacobi sequences with period pq over an extension field of the odd prime field F_r. Our method is based on the use of a pqth root of unity over the extension field, and the representation of the Jacobi sequences by corresponding indicator functions and quadratic characters of two primes p and q.