Weight hierarchies of a family of linear codes associated with degenerate quadratic forms

04/18/2018

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We restrict the degenerate quadratic forms of a finite field to its subspaces and quotient spaces. And some related results on the subspaces and quotient spaces are obtained. Based on this, we solve the weight hierarchies of a family of linear codes relating to these degenerate quadratic forms.

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Weight hierarchies of a family of linear codes associated with degenerate quadratic forms

Weight hierarchies of three-weight p-ary linear codes from inhomogeneous quadratic forms

Two theorems on distribution of Gaussian quadratic forms

Stolarsky's invariance principle for finite metric spaces

Generalized Hamming Weights of Linear Codes from Quadratic Forms over Finite Fields of Even Characteristic

Optimization of Real, Hermitian Quadratic Forms: Real, Complex Hopfield-Amari Neural Network

Explicit equivalence of quadratic forms over F_q(t)

Shifted Lanczos method for quadratic forms with Hermitian matrix resolvents

Weight hierarchies of a family of linear codes associated with degenerate quadratic forms

Related Research

Weight hierarchies of three-weight p-ary linear codes from inhomogeneous quadratic forms

Two theorems on distribution of Gaussian quadratic forms

Stolarsky's invariance principle for finite metric spaces

Generalized Hamming Weights of Linear Codes from Quadratic Forms over Finite Fields of Even Characteristic

Optimization of Real, Hermitian Quadratic Forms: Real, Complex Hopfield-Amari Neural Network

Explicit equivalence of quadratic forms over F_q(t)

Shifted Lanczos method for quadratic forms with Hermitian matrix resolvents