X. Kai and S. Zhu in the paper "On cyclic self-dual codes", AAECC, vol. 19, pp. 509-525, 2008, at page 510 in line 6 said that, It is well Known that there are no cyclic self-dual codes over $F_q$ when $q$ is odd.
I know that W. Cary Huffman and V. Pless in the book "Fundamentals of error correcting codes" proved that there are no self-dual cyclic codes of length $n$ over $F_q$ when $gcd(n,q)=1$.
Also Y. Jia, S. Ling and C. Xing in the paper with name "On self-dual cyclic codes over finite fields" at 2011 proved that there exist at least one self-dual cyclic code of length $n$ over $F_q$ if and only if $q$ is a power of $2$ and $n$ is even.
My questions are:
1) Where can I find the proof of the claim that introduced in my first paragraph?
2) Generally, how can I find some good sources about self-dual (self-orthogonal) cyclic codes, precisely about the existence of these codes over finite fields?