Mac Williams identities and polarized Riemann-Roch conditions
Azniv Kasparian, Ivan Marinov
TL;DR
This paper demonstrates that Mac Williams identities for additive codes are equivalent to polarized Riemann-Roch conditions on their Zeta-functions, linking code duality to Serre duality in algebraic geometry.
Contribution
It establishes a novel equivalence between coding theory identities and geometric Riemann-Roch conditions, revealing a deep duality connection.
Findings
Mac Williams identities are equivalent to polarized Riemann-Roch conditions.
Duality of additive codes corresponds to Serre duality.
Provides a geometric interpretation of code duality.
Abstract
The present note establishes the equivalence of Mac Williams identities for an additive code C and its dual to Polarized Riemann-Roch Conditions on their Zeta-functions. In such a way, the duality of additive codes appears to be a polarized form of the Serre duality on a smooth irreducible projective curve.
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · Algebraic structures and combinatorial models