Some cyclic codes of prime-power length (Q496127)

Summary: A new class of cyclic codes of length \(2^n\) over \(\mathrm{GF}(q)\) is proposed, where \(q\) is a prime of the form \(8m\pm 3\) and \(n > 3\) is an integer. These codes are defined in terms of their generator polynomials. These codes have many properties analogous to those of duadic codes. Generator polynomials of some duadic codes of length \(p^n\) over \(\mathrm{GF}(q)\) are also discussed, where \(p\) is an odd prime, \(n\) is an integer and \(q = \rho\) or \(\rho^2\) for some prime \(\rho\).