Self-Orthogonal Cyclic Codes and Complementary-dual Cyclic Codes of Length pnqm over Fl
Xingxing Chang
Common Courses Department, Hubei Industrial Polytechnic, Shiyan, Hubei 442000, China.
Jian Gao *
Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China.
*Author to whom correspondence should be addressed.
Abstract
Let 
and 
where p , q , I are distinct odd
primes, I is a primitive root both modulo Pn and 
.We obtain explicit expressions for all dmn + m + n + 1 I -cyclotomic cosets modulo Pn qm We explicitly determine generating polynomials and enumeration formulas of all self-orthogonal cyclic codes and complementary-dual cyclic codes of length Pn qm fI As an example, we give all self orthogonal cyclic codes and complementary-dual cyclic codes of length 175 over F3.
Keywords: Cyclotomic cosets, self-orthogonal, complementary-dual cyclic codes