An analogue of the Pless symmetry codes

Symmetry Codes and Their Invariant Subcodes

Self-dual codes over GF(7)

This paper studies self-dual and maximal self-orthogonal codes over GF(3). First, a number of Gleason-type theorems are given, describing the weight enumerators of such codes. Second, a table of all such codes of length _-<12 is constructed. Finally, the complete weight enumerators of various quadratic residue and symmetry codes of length =<60.are obtained.

Double circulant codes from two class association schemes

Two class association schemes consist of either strongly regular graphs (SRG) or doubly regular tournaments (DRT). We construct self-dual codes from the adjacency matrices of these schemes. This generalizes the construction of Pless ternary Symmetry codes, Karlin binary Double Circulant codes, Calderbank and Sloane quaternary double circulant codes, and Gaborit Quadratic Double Circulant codes ...

Calculations of Dihedral Groups Using Circular Indexation

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...

The Binary Self-Dual Codes of Length up to 32: A Revised Enumeration

This paper presents a revised enumeration of the binary self-dual codes of length up to 32 given by Conway and Pless in 1978-1980. The list of 85 doubly-even selfdual codes of length 32 is essentially correct, but several of their descriptions need amending. The principal change is that there are 731 (not 664) inequivalent selfdual codes of length 30. Furthermore, there are three (not two) [28,...