Symplectic spread-based generalized Kerdock codes

DOI10.1007/s10623-006-9031-8zbMath1138.94018OpenAlexW2033039345MaRDI QIDQ2383996

Consuelo Martínez, Ignacio F. Rúa, Santos González

Publication date: 20 September 2007

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-006-9031-8

zbMATH Keywords

Galois ring(Generalized) Kerdock codeFinite (Pre)SemifieldLinear presentation of codesSymplectic spread

Mathematics Subject Classification ID

Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Spreads and packing problems in finite geometry (51E23) Other types of codes (94B60) Polar geometry, symplectic spaces, orthogonal spaces (51A50) Finite commutative rings (13M99)

Related Items (8)

Symmetric bilinear forms over finite fields of even characteristic ⋮ Commutative Semifields of Order 3⁵ ⋮ NONBINARY DELSARTE–GOETHALS CODES AND FINITE SEMIFIELDS ⋮ Witt's theorems for Galois ring valued quadratic forms ⋮ Finite semifields with 7⁴elements ⋮ New advances in the computational exploration of semifields ⋮ Witt index for Galois ring valued quadratic forms ⋮ Classification of semifields of order 64

Cites Work

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• Finite semifields and projective planes
• Generalizations of the Kervaire invariant
• Minimum-weight codewords as generators of generalized Reed-Muller codes
• Construction of noise-resistant codes by means of linear recurrences over Galois rings
• A class of low-rate nonlinear binary codes
• Spreads, Translation Planes and Kerdock Sets. I
• Witt's Extension Theorem for mod Four Valued Quadratic Forms
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• Z₄ -Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets
• Symplectic semifield planes and ℤ₄–linear codes
• On Z/sub 4/-duality
• Linearly representable codes and the Kerdock code over an arbitrary Galois field of characteristic 2
• A class of optimum nonlinear double-error-correcting codes
• Complete weight enumerators of generalized Kerdock code and related linear codes over Galois ring
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