Search

In this paper, we give the structures of all ( 1 + u + v ) -constacyclic codes of length 2 s over F 2 + u F 2 + v F 2 + u v F 2 , we also obtain the number of codewords, and the dual of each constacyclic code. Among other results, we study the form of such constacyclic codes that are self-dual and give the number of these codes. We end by giving all self-dual constacyclic codes of length 2, 4 and 8. [ABSTRACT FROM AUTHOR]

Let q be a power of an odd prime, and be the trace mapping. A mapping is called planar (or perfect nonlinear) on if for any non-zero , the difference mapping is a permutation where for , . Kyureghyan and Özbudak (2012) [8] considered the planarity of mappings on for and proved that there is no planar for . For the case and , they raised three conjectures. In this paper we prove the third conjecture which says that there is no planar for , by using Kloosterman sums. Our proof also works for case , so we present a new proof of the Kyureghyan–Özbudak result. For case , we present an elementary proof of the first conjecture which says that there is no planar for . [ABSTRACT FROM AUTHOR]

In this paper, we explicitly determine the generator polynomials of all repeated-root constacyclic codes of length n l p s over F q and their dual codes, where l is an odd prime different from p , and n is an odd prime different from both l and p such that n = 2 h + 1 for some prime h or h = 1 . Moreover, we give all self-dual cyclic codes of length n l p s over F q and their enumeration. All linear complementary dual (LCD) cyclic codes of length n l p s over F q and their enumeration are also obtained. [ABSTRACT FROM AUTHOR]