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Let α be a primitive element of a finite field Fr, where r=qm1m2 and gcd(m1,m2)=d, so α1=αr−1qm1−1 and α2=αr−1qm2−1 are primitive elements of Fqm1 and Fqm2, respectively. Let e be a positive integer such that gcd(e,qm2−1qd−1)=1, Fqm2=Fq(α2e), and α1 and α2e are not conjugates over Fq. We define a cyclic codeC={c(a,b):a∈Fqm1,b∈Fqm2},c(a,b)=(T1(aα1i)+T2(bα2ei))i=0n−1, where Ti denotes the trace function...
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