Finite fields
On the Algebraic Structure of Quasi-cyclic Codes II: Chain Rings
Designs, Codes and Cryptography
IEEE Transactions on Information Theory
Type II codes, even unimodular lattices, and invariant rings
IEEE Transactions on Information Theory
On the algebraic structure of quasi-cyclic codes .I. Finite fields
IEEE Transactions on Information Theory
On existence of good self-dual quasicyclic codes
IEEE Transactions on Information Theory
On the algebraic structure of quasi-cyclic codes III: generator theory
IEEE Transactions on Information Theory
On self-orthogonal group ring codes
Designs, Codes and Cryptography
Constacyclic codes of length 2sover Galois extension rings of F2 + uF2
IEEE Transactions on Information Theory
Quasi-cyclic codes with cyclic constituent codes
Finite Fields and Their Applications
| Hi-index | 0.06 |
A trace formula for quasi-cyclic codes over rings of characteristic not coprime with the co-index is derived. The main working tool is the Generalized Discrete Fourier Transform (GDFT), which in turn relies on the Hasse derivative of polynomials. A characterization of Type II self-dual quasi-cyclic codes of singly even co-index over finite fields of even characteristic follows. Implications for generator theory are shown. Explicit expressions for the combinatorial duocubic, duoquintic and duoseptic constructions in characteristic two over finite fields are given.