Recent progress in algebraic design theory

Authors:
Qing Xiang
Affiliations:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
Venue:
Finite Fields and Their Applications
Year:
2005

Citing 40
Cited 9

A family of difference sets having—1 as an invariant

European Journal of Combinatorics
A diagonal form for the incidence matrices of t-subsets vs. k-subsets

European Journal of Combinatorics
Difference sets in Abelian 2-groups

Journal of Combinatorial Theory Series A
Proof of a conjecture of Hadamard 2-groups

Journal of Combinatorial Theory Series A
An exponent bound on skew Hadamard abelian difference sets

Designs, Codes and Cryptography
Non-Abelian Hadamard difference sets

Journal of Combinatorial Theory Series A
Some new difference sets

Journal of Combinatorial Theory Series A
On the classification of geometric codes by polynomial functions

Designs, Codes and Cryptography
On difference sets in groups of order 4p2

Journal of Combinatorial Theory Series A
Spreads in Strongly Regular Graphs

Designs, Codes and Cryptography - Special issue dedicated to Hanfried Lenz
A result on Ma's conjecture

Journal of Combinatorial Theory Series A
Finite fields

Finite fields
Planar Functions and Planes of Lenz-Barlotti Class II

Designs, Codes and Cryptography
Constructions of Hadamard difference sets

Journal of Combinatorial Theory Series A
A unifying construction for difference sets

Journal of Combinatorial Theory Series A
Difference Sets with n = 2p^m

Journal of Algebraic Combinatorics: An International Journal
Difference Sets and Hyperovals

Designs, Codes and Cryptography
Gauss sums, Jacobi sums, and p-ranks of cyclic difference sets

Journal of Combinatorial Theory Series A
Multiplicative Difference Sets via Additive Characters

Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
Signed Hypergraph Designs and Diagonal Forms for Some IncidenceMatrices

Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
Note on GMW designs

European Journal of Combinatorics
Maximal arcs in projective three-spaces and double-error-correcting cyclic codes

Journal of Combinatorial Theory Series A
A New Family of Ternary Sequences with IdealTwo-level Autocorrelation Function

Designs, Codes and Cryptography
The Existence of a Bush-Type Hadamard Matrix of Order 324 and Two New Infinite Classes of Symmetric Designs

Designs, Codes and Cryptography
The existence of a Bush-type Hadamard matrix of order 36 and two new infinite classes of symmetric designs

Journal of Combinatorial Theory Series A
A New Family of Cyclic Difference Sets with Singer Parameters in Characteristic Three

Designs, Codes and Cryptography
Projective geometric codes

Journal of Combinatorial Theory Series A
A root graph that is locally the line graph of the Petersen graph

Discrete Mathematics - The 2000 Com2MaC conference on association schemes, codes and designs
The invariant factors of some cyclic difference sets

Journal of Combinatorial Theory Series A
Cyclic Relative Difference Sets and their p-Ranks

Designs, Codes and Cryptography
On the p-Ranks and Characteristic Polynomials of Cyclic Difference Sets

Designs, Codes and Cryptography
New Cyclic Difference Sets with Singer Parameters Constructed from d-Homogeneous Functions

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The Field Descent Method

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A recursive construction for new symmetric designs

Designs, Codes and Cryptography
Binary pseudorandom sequences of period 2n-1 with ideal autocorrelation

IEEE Transactions on Information Theory
Binary pseudorandom sequences of period 2m-1 with ideal autocorrelation generated by the polynomial zd+(z+1)d

IEEE Transactions on Information Theory
On balanced binary sequences with two-level autocorrelation functions

IEEE Transactions on Information Theory
On cyclic codes that are invariant under the general linear group

IEEE Transactions on Information Theory
On the Existence of Abelian Hadamard Difference Sets and a New Family of Difference Sets

Finite Fields and Their Applications
New cyclic difference sets with Singer parameters

Finite Fields and Their Applications

Skew Hadamard difference sets from the Ree--Tits slice symplectic spreads in PG(3,32h+1)

Journal of Combinatorial Theory Series A
Efficient matrix rank computation with application to the study of strongly regular graphs

Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Pseudo-Paley graphs and skew Hadamard difference sets from presemifields

Designs, Codes and Cryptography
Large matrix, small rank

Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Special subsets of difference sets with particular emphasis on skew Hadamard difference sets

Designs, Codes and Cryptography
Non-abelian skew Hadamard difference sets fixed by a prescribed automorphism

Journal of Combinatorial Theory Series A
Cyclotomic constructions of skew Hadamard difference sets

Journal of Combinatorial Theory Series A
Sequences and functions derived from projective planes and their difference sets

WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
Cyclotomy, gauss sums, difference sets and strongly regular cayley graphs

SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications

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Abstract

We survey recent results on difference sets, p-ranks and Smith normal forms of certain set-inclusion matrices and subspace-inclusion matrices.