How many weights can a linear code have?
| Autor: | Hongwei Zhu, Gérard D. Cohen, Minjia Shi, Patrick Solé |
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| Přispěvatelé: | Anhui University [Hefei], Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), Télécom ParisTech |
| Rok vydání: | 2018 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Information Theory Information Theory (cs.IT) Applied Mathematics Dimension (graph theory) 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology Function (mathematics) 01 natural sciences Upper and lower bounds Linear code Computer Science Applications Combinatorics Nonlinear system 010201 computation theory & mathematics [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] 0202 electrical engineering electronic engineering information engineering Mathematics |
| Zdroj: | Designs, Codes and Cryptography Designs, Codes and Cryptography, Springer Verlag, 2019, ⟨10.1007/s10623-018-0488-z⟩ |
| ISSN: | 1573-7586 0925-1022 |
| Popis: | We study the combinatorial function L(k, q), the maximum number of nonzero weights a linear code of dimension k over $${\mathbb {F}}_q$$ can have. We determine it completely for $$q=2,$$ and for $$k=2,$$ and provide upper and lower bounds in the general case when both k and q are $$\ge 3.$$ A refinement L(n, k, q), as well as nonlinear analogues N(M, q) and N(n, M, q), are also introduced and studied. |
| Databáze: | OpenAIRE |
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