Strong difference families, difference covers, and their applications for relative difference families

DOI10.1007/s10623-008-9259-6zbMath1247.05035OpenAlexW2028683584MaRDI QIDQ1009156

Koji Momihara

Publication date: 31 March 2009

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

Full work available at URL: https://doi.org/10.1007/s10623-008-9259-6

zbMATH Keywords

Optical orthogonal codesSums of squaresCyclotomDifference coversPartial difference setsRelative difference familiesStrong difference families

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Combinatorial codes (94B25)

Related Items (24)

Cyclic balanced sampling plans excluding contiguous units with block size four ⋮ Some infinite classes of optimal \({(v,\{3,4\},1,Q)}\)-OOCs with \({Q\in\{(\frac{1}{3},\frac{2}{3}),(\frac{2}{3},\frac{1}{3})\}}\) ⋮ Bounds and Constructions on (v, 4, 3, 2) Optical Orthogonal Codes ⋮ Constructions of optimal variable-weight OOCs via quadratic residues ⋮ Partitioned difference families and harmonious linear spaces ⋮ Constructions for optimal \((u\times v,\{3,4\},1,Q)\)-OOSPCs ⋮ Balanced \(( \mathbb{Z}_{2u}\times \mathbb{Z}_{38v}, \{3, 4, 5\}, 1)\) difference packings and related codes ⋮ Existence of strong difference families and constructions for eight new 2‐designs ⋮ New 2-designs from strong difference families ⋮ New results on optimal \((v,4,2,1)\) optical orthogonal codes ⋮ On optimal (Z6m×Z6n,4,1) and (Z2m×Z18n,4,1) difference packings and their related codes ⋮ Partitionable sets, almost partitionable sets, and their applications ⋮ Further results on optimal \((v,4,2,1)\)-OOCs ⋮ On balanced \(( \mathbb{Z}_{4 u} \times \mathbb{Z}_{8 v}, \{4, 5 \}, 1)\) difference packings ⋮ Bounds and constructions for optimal \((n, \{3, 5 \}, \varLambda_a, 1, Q)\)-OOCs ⋮ Combinatorial constructions for optimal multiple-weight optical orthogonal signature pattern codes ⋮ The first families of highly symmetric Kirkman triple systems whose orders fill a congruence class ⋮ Some 20-regular CDP(5,1;20\(u\)) and their applications ⋮ On silver and golden optical orthogonal codes ⋮ Frame difference families and resolvable balanced incomplete block designs ⋮ Strong difference families of special types ⋮ Hadamard partitioned difference families and their descendants ⋮ Super-regular Steiner 2-designs ⋮ Compatible difference packing set systems and their applications to multilength variable-weight OOCs

Cites Work

• New negative Latin square type partial difference sets in nonelementary Abelian 2-groups and 3-groups
• Combinatorial designs and the theorem of Weil on multiplicative character sums
• Supplementary difference sets and Jacobi sums
• A survey of partial difference sets
• Partial difference sets in \(p\)-groups
• Starters and related codes
• Some combinatorial constructions for optical orthogonal codes
• Cyclic designs with block size 4 and related optimal optical orthogonal codes
• Proper partial geometries with Singer groups and pseudogeometric partial difference sets
• New Hadamard matrices of order \(4p^{2}\) obtained from Jacobi sums of order 16
• Cyclotomy and difference families in elementary Abelian groups
• Constructions of partial difference sets and relative difference sets using Galois rings. II
• Optical orthogonal codes: their bounds and new optimal constructions
• Optimal (9v, 4, 1) Optical Orthogonal Codes
• Optimal (4up, 5, 1) optical orthogonal codes
• A New Class of Optimal Optical Orthogonal Codes With Weight Five
• Strong difference families over arbitrary graphs
• Optical orthogonal codes: design, analysis and applications
• Constructions for optimal (υ, 4, 1) optical orthogonal codes
• Combinatorial constructions of optimal optical orthogonal codes with weight 4
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Strong difference families, difference covers, and their applications for relative difference families