Twisted Group Codes
Javier de la Cruz, Wolfgang M. Willems
Abstract
We investigate right ideals as codes in twisted group algebras. Such codes are called twisted group codes. It turns out that many interesting codes belong to this class; for instance, the ternary extended Golay code, Hamming codes and constacyclic codes. In particular we characterize all linear codes which are twisted group codes in terms of their automorphism group.
Topics & Concepts
Linear codeHamming codeBlock codeGroup codeBinary Golay codeRaptor codeMathematicsDiscrete mathematicsGroup (periodic table)Luby transform codeTernary Golay codeTornado codeCombinatoricsAutomorphism groupFountain codeReed–Muller codeAutomorphismAlgorithmDecoding methodsPhysicsQuantum mechanicsCoding theory and cryptographyCooperative Communication and Network CodingFinite Group Theory Research