Higher weights and near-MDR codes over chain rings | Zendy

Zihui Liu | Zendy; Liao Da-jian | Zendy

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Higher weights and near-MDR codes over chain rings

Author(s) -

Zihui Liu,

Liao Da-jian

Publication year - 2018

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2018045

Subject(s) - mathematics , chain (unit) , combinatorics , pure mathematics , physics , astronomy

The matrix description of a near-MDR code is given, and some judging criterions are presented for near-MDR codes. We also give the weight distribution of a near-MDR code and the applications of a near-MDR code to secret sharing schemes. Furthermore, we will introduce the chain condition for free codes over finite chain rings, and then present a formula for computing higher weights of tensor product of free codes satisfying the chain condition. We will also find a chain for any near-MDR code, and thus show that any near-MDR code satisfies the chain condition.

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