On the Weight Hierarchy of Product Codes

Authors:
Conchita Martínez-Pérez;Wolfgang Willems
Affiliations:
Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain conmar@posta.unizar.es;Fakultät für Mathematik, Otto-von-Guericke-Universität, D 39106 Magdeburg, Germany wolfgang.willems@mathematik.uni-magdeburg.de
Venue:
Designs, Codes and Cryptography
Year:
2004

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Abstract

Let V and W be codes and let C = V ⊗ W be the product code of V and W. In [6] Wei and Yang, conjectured a formula for the generalized Hamming weights of V ⊗ W in terms of those of V and W provided that both V and W satisfy the chain condition. Recently the conjecture has been proved by Schaathun [4]. In this paper we generalize the formula to a product code with more than two components.