Weight distribution of Hermitian codes and matrices rank

Pellegrini, Marco; Sala, Massimiliano

doi:10.1016/j.ffa.2019.101578

Cited by 3 publications

(2 citation statements)

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“…In [PS19], the authors prove that there exist linear relations among the weights of Hermitian codes. Moreover, they prove that the knowledge of A d , .…”

Section: Hermitian Codesmentioning

confidence: 99%

“…the number of minimum-weight words) in [DL95]. Some classes of codes (whose enumerator is still unknown) have received considerable attention, such as the Hermitian codes ([Duu99, BM00, MPS16, MR19]), where recently, in [PS19], it has been found out that the computation of their distributions may be significantly less hard than it appeared .…”

Section: Introductionmentioning

confidence: 99%

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A formula on the weight distribution of linear codes with applications to AMDS codes

Meneghetti¹,

Pellegrini²,

Sala³

2020

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The determination of the weight distribution of linear codes has been a fascinating problem since the very beginning of coding theory. There has been a lot of research on weight enumerators of special cases, such as self-dual codes and codes with small Singleton's defect. We propose a new set of linear relations that must be satisfied by the coefficients of the weight distribution. From these relations we are able to derive known identities (in an easier way) for interesting cases, such as extremal codes, Hermitian codes, MDS and NMDS codes. Moreover, we are able to present for the first time the weight distribution of AMDS codes. We also discuss the link between our results and the Pless equations.

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“…In [PS19], the authors prove that there exist linear relations among the weights of Hermitian codes. Moreover, they prove that the knowledge of A d , .…”

Section: Hermitian Codesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%