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RESEARCH PRODUCT

New lower bounds for the minimum distance of generalized algebraic geometry codes

Alberto Picone

subject

Discrete mathematicsAlgebraic cycleBlock codeAlgebraic function field generalized algebraic geometry codes minimum distanceAlgebra and Number TheoryDerived algebraic geometryFunction field of an algebraic varietyAlgebraic surfaceReal algebraic geometryDimension of an algebraic varietySettore MAT/03 - GeometriaLinear codeMathematics

description

Abstract In this paper, we give a new lower bound for generalized algebraic geometry codes with which we are able to construct some new linear codes having better parameters compared with the ones known in the literature. Moreover, we give a relationship between a family of generalized algebraic geometry codes and algebraic geometry codes. Finally, we propose a decoding algorithm for such a family.

yearjournalcountryeditionlanguage
2013-06-01Journal of Pure and Applied Algebra
https://doi.org/10.1016/j.jpaa.2012.10.004