We are interested in calculating the weight distribution of Hermitian codes over the finite field with q2 elements. In this work we show that, if we can compute the partial weight distribution for about q2 weights, then we will easily compute the whole weight distribution (which has about q3 values). To achieve this, we actually show that the computation of a given element of the weight distribution is equivalent to a less laborious task, which is the classification of some submatrices of the parity-check matrix according to their rank.

Weight distribution of Hermitian codes and matrices rank / Pellegrini, M.; Sala, M.. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - 60:(2019), pp. 10157801-10157817. [10.1016/j.ffa.2019.101578]

Weight distribution of Hermitian codes and matrices rank

Pellegrini M.;Sala M.
2019-01-01

Abstract

We are interested in calculating the weight distribution of Hermitian codes over the finite field with q2 elements. In this work we show that, if we can compute the partial weight distribution for about q2 weights, then we will easily compute the whole weight distribution (which has about q3 values). To achieve this, we actually show that the computation of a given element of the weight distribution is equivalent to a less laborious task, which is the classification of some submatrices of the parity-check matrix according to their rank.
2019
Pellegrini, M.; Sala, M.
Weight distribution of Hermitian codes and matrices rank / Pellegrini, M.; Sala, M.. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - 60:(2019), pp. 10157801-10157817. [10.1016/j.ffa.2019.101578]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/297825
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