A New Family of Optimal Binary Few-Weight Codes From Simplicial Complexes
Xiaoxiao Li, Minjia Shi
Abstract
Trace codes over a cubic ring extension of the binary field are constructed by using a triple of simplicial complexes. A linear Gray map yields several infinite families of binary few-weight codes which can have as many as 9 weights. By equating two complexes in the triple, we obtain binary three-weight codes, which are minimal and distance optimal.
Topics & Concepts
Binary numberMathematicsExtension (predicate logic)CombinatoricsTRACE (psycholinguistics)Linear codeBinary codeDiscrete mathematicsBlock codeComputer scienceAlgorithmArithmeticDecoding methodsPhilosophyProgramming languageLinguisticsCoding theory and cryptographygraph theory and CDMA systemsCellular Automata and Applications