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A survey of partial difference sets
  • S. L. Ma
  • Mathematics, Computer Science
  • Des. Codes Cryptogr.
  • 1 July 1994
In this survey, it is tried to list all important existence and nonexistence results concerning partial difference sets, e.g., constructions using partial congruence partitions, quadratic forms, cyclotomic classes and finite local rings. Expand
Partial difference sets
  • S. L. Ma
  • Computer Science, Mathematics
  • Discret. Math.
  • 1 March 1984
A (?,k,?,β)-partial difference set in a finite group G of order ? is a subset D of G with k distinct elements such that expressions dnd?12 for d1 and d2 in D, represent each non-identity element notExpand
On non-existence of perfect and nearly perfect sequences
We study the complex p-ary perfect and nearly perfect sequences where p is an odd prime and show that the existence of such sequences is equivalent to the existence of certain kinds of differenceExpand
Polynomial addition sets
Constructions of Partial Difference Sets and Relative Difference Sets on p-Groups
By using some finite local rings, we construct some new partial difference sets and relative difference sets on ^-groups where p is any prime. When p = 2, some of the partial difference setsExpand
Planar Functions, Relative Difference Sets, and Character Theory
Planar functions from2nto3nare studied in this paper. By investigating the character values of the corresponding relative difference sets, we obtain some nonexistence results of planar functions. InExpand
The structure of Schur rings over cyclic groups
Abstract Let G be a finite group and D 1 , D 2 ,…, D d be a partition of G . Suppose, for each i =1,2,…, d , { gϵG ∣ g -1 ϵD i };= D j for some j depending on i ; and D i D j =∑ d h=1 P h ij D h forExpand
A note on binary arrays with a certain window property
  • S. L. Ma
  • Mathematics, Computer Science
  • IEEE Trans. Inf. Theory
  • 1 September 1984
For some rs = 2^{mn} , there exist periodic r \times s binary arrays such that all m \times n binary matrices will appear in it. As two-dimensional versions of de Bruijn sequences, these kinds ofExpand
Study of proper circulant weighing matrices with weight 9
We provide the first theoretical proof of the spectrum of orders n for which circulant weighing matrices with weight 9 exist. This spectrum consists of those positive integers n, which are multiplesExpand