Weight hierarchies of a family of linear codes associated with degenerate quadratic forms
Abstract
We restrict a degenerate quadratic form f over a finite field of odd characteristic to subspaces. Thus, a quotient space related to f is introduced. Then we get a non-degenerate quadratic form induced by f over the quotient space. Some related results on the subspaces and quotient space are obtained. Based on this, we solve the weight hierarchies of a family of linear codes related to f.
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