Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized weights: an anticode approach   In this paper we study generalized weights as an algebraic invariant of a
code. We first describe anticodes in the Hamming and in the rank metric,
proving in particular that optimal anticodes in the rank metric coincide with
Frobenius-closed spaces. Then we characterize both generalized Hamming and rank
weights of a code in terms of the intersection of the code with optimal
anticodes in the respective metrics. Inspired by this description, we propose a
new algebraic invariant, which we call "Delsarte generalized weights", for
Delsarte rank-metric codes based on optimal anticodes of matrices. We show that
our invariant refines the generalized rank weights for Gabidulin codes proposed
by Kurihara, Matsumoto and Uyematsu, and establish a series of properties of
Delsarte generalized weights. In particular, we characterize Delsarte optimal
codes and anticodes in terms of their generalized weights. We also present a
duality theory for the new algebraic invariant, proving that the Delsarte
generalized weights of a code completely determine the Delsarte generalized
weights of the dual code. Our results extend the theory of generalized rank
weights for Gabidulin codes. Finally, we prove the analogue for Gabidulin codes
of a theorem of Wei, proving that their generalized rank weights characterize
the worst-case security drops of a Gabidulin rank-metric code.

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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
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The categories of this paper are: eess
3
The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol