Weight Hierarchies of a Class of Linear Codes Related to Non-Degenerate Quadratic Forms
Fei Li
Abstract
We restrict quadratic forms to subspaces of finite fields and obtain some interesting results about dual spaces. On this basis, we solve the weight hierarchies of a class of linear codes associated with non-degenerate quadratic forms.
Topics & Concepts
MathematicsLinear subspaceClass (philosophy)Finite fieldQuadratic equationDiscrete mathematicsCombinatoricsLinear codeHamming weightMinimum weightBinary quadratic formFinite setAlgebra over a fieldDual (grammatical number)Code (set theory)New classQuadratic residueQuadratic form (statistics)Block codeQuadratic fieldCoding theory and cryptographyFinite Group Theory ResearchCryptography and Residue Arithmetic