On near-MDS codes
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Publication:1904252
DOI10.1007/BF01222850zbMath0849.94023OpenAlexW1530125006MaRDI QIDQ1904252
Stefan Dodunekov, Ivan N. Landgev
Publication date: 19 December 1995
Published in: Journal of Geometry (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01222850
linear codescombinatorial designsnear-MDS codesarcs in finite projective planesmaximum-distance-separable codes
Other designs, configurations (05B30) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Other finite incidence structures (geometric aspects) (51E30)
Related Items (44)
Higher weights and near-MDR codes over chain rings ⋮ Complete \((k,3)\)-arcs from quartic curves ⋮ Near-MDS codes from elliptic curves ⋮ A class of twisted generalized Reed-Solomon codes ⋮ Onm-MDS codes over finite fields ⋮ MDS and near-MDS codes via twisted Reed-Solomon codes ⋮ Near MDS codes from oval polynomials ⋮ A formula on the weight distribution of linear codes with applications to AMDS codes ⋮ A class of almost MDS codes ⋮ The minimum locality of linear codes ⋮ On Hamming distance distributions of repeated-root constacyclic codes of length \(3p^s\) over \(\mathbb{F}_{p^m} + u \mathbb{F}_{p^m}\) ⋮ NNMDS codes ⋮ Near MDS codes of non-elliptic-curve type from Reed-Solomon codes ⋮ Duursma's reduced polynomial ⋮ New classes of NMDS codes with dimension 3 ⋮ Construction of self-dual codes over finite rings \(\mathbb Z_{p^m}\) ⋮ The properties and the error-correcting pair for lengthened GRS codes ⋮ A class of double-twisted generalized Reed-Solomon codes ⋮ Maximal AMDS codes ⋮ MDS or NMDS LCD codes from twisted Reed-Solomon codes ⋮ Duality of generalized twisted Reed-Solomon codes and Hermitian self-dual MDS or NMDS codes ⋮ Near MDS codes with dimension 4 and their application in locally recoverable codes ⋮ The \((+)\)-extended twisted generalized Reed-Solomon code ⋮ Near-MDS codes from maximal arcs in \(\mathrm{PG}(2,q)\) ⋮ On near-MDS codes and caps ⋮ Constructions of near MDS codes which are optimal locally recoverable codes ⋮ Euclidean and Hermitian self-dual MDS codes over large finite fields. ⋮ Quasi-cyclic NMDS codes ⋮ MDS or NMDS self-dual codes from twisted generalized Reed-Solomon codes ⋮ On the completeness of certain \(n\)-tracks arising from elliptic curves ⋮ Almost MDS codes ⋮ MacWilliams extension theorem for MDS codes over a vector space alphabet ⋮ A survey on proper codes ⋮ On the completeness of plane cubic curves over finite fields ⋮ The non-existence of some NMDS codes and the extremal sizes of complete \((n,3)\)-arcs in \(\mathrm{PG}(2,16)\) ⋮ Maximal (\(n\),3)-arcs in PG(2,13) ⋮ A Riemann hypothesis analogue for near-MDS codes ⋮ The smallest size of a complete cap in PG(3,\,7) ⋮ Some optimal cyclic \(\mathbb{F}_q\)-linear \(\mathbb{F}_{q^t}\)-codes ⋮ Elliptic near-MDS codes over \(\mathbb{F}_5\) ⋮ Схема разделения секрета типа схемы Блэкли, основанная на пересечении подпространств ⋮ Near-MDS codes arising from algebraic curves ⋮ The packing problem in statistics, coding theory and finite projective spaces ⋮ Matrix characterization of linear codes with arbitrary Hamming weight hierarchy
Cites Work
- A comment on the weight structure of generator matrices of linear codes
- Some results concerning \(\{(q+1)(n-1);\;n\}\)-arcs and \(\{(q+1)\;(n-1)+1;\;n\}\)-arcs in finite projective planes of order \(q\)
- The Geometry of Two-Weight Codes
- Generalized Hamming weights for linear codes
- New 5-designs
- A Bound for Error-Correcting Codes
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