Perfect Ternary Arrays

  title={Perfect Ternary Arrays},
  author={K. T. Arasu and John F. Dillon},
A perfect ternary array is an r-dimensional array with entries 0, +1 and —1 such that all of its out-of-phase periodic autocorrelation coefficients are zero. Such an array is equivalent to a group developed weighing matrix. These can therefore be considered as elements in the group ring ℤG for a suitable abelian group G. Using this approach, we provide a comprehensive survey of these objects, restricting our attention mostly to the one-and two-dimensional (so called cyclic and bicyclic) cases. 
Group developed weighing matrices
The question of existence for 318 weighing matrices of order and weight both below 100 is answered, and some of the new results provide insight into the existence of matrices with larger weights and orders. Expand
Retrospective Review of Perfect Ternary Sequences and Their Generators
  • E. Krengel
  • Mathematics
  • Journal of the Russian Universities. Radioelectronics
  • 2019
Introduction. Perfect polyphase unimodular sequences, i. e. sequences with ideal periodic autocorrelation and single amplitude of symbols are widely used in modern radio communications and radar. AExpand
Circulant weighing matrices of weight 22t
A complete computer search is made for all circulant weighing matrices of order 16 such that MMT = kIn for some positive integer t and new structural results are obtained. Expand
An Investigation of Group Developed Weighing Matrices
Hollon, Je R. M.S., Department of Mathematics and Statistics, Wright State University, 2010. An Investigation of Group Developed Weighing Matrices. A weighing matrix is a square matrix whose entriesExpand
Perfect Sequences and Arrays of Unbounded Lengths and Sizes over the Basic Quaternions
The aim of this Thesis is to provide new understanding of the existence of perfect sequences and arrays over the alphabets of quaternions and complex numbers, and multi-dimensional arrays withExpand
Structure of group invariant weighing matrices of small weight
Abstract We show that every weighing matrix of weight n invariant under a finite abelian group G can be generated from a subgroup H of G with | H | ≤ 2 n − 1 . Furthermore, if n is an odd prime powerExpand
Finiteness of circulant weighing matrices of fixed weight
It is shown that, for every odd prime power q, there are at most finitely many proper circulant weighing matrices of weight q. Expand
Circulant weighing matrices whose order and weight are products of powers of 2 and 3
All circulant weighing matrices whose order and weight are products of powers of 2 and 3 are classified and it is shown that proper CW(v,36)@?s exist for all v=0(mod48), all of which are new. Expand
Symmetric Weighing Matrices Constructed using Group Matrices
It is proved that there is no symmetric abelian group weighing matrices of order 2pr and weight p2 where p is a prime and p≥ 5. Expand
Permutations with a distinct di ! erence property
The topic of this paper arose out of a consideration of Costas sequences, which are used in sonar and radar applications. These sequences have the de/ning property that all di!erences of elements theExpand


Perfect ternary arrays
Four synthesizing methods for perfect ternary arrays are presented and new strong conditions for the existence of perfect arrays are developed, which can be used as starting arrays to construct additional perfect terNary sequences and arrays. Expand
Generalized perfect arrays and menon difference sets
  • J. Jedwab
  • Mathematics, Computer Science
  • Des. Codes Cryptogr.
  • 1992
It is shown that a generalized PBA whose type is not (0, ..., 0) is equivalent to a relative difference set in an abelian factor group, and several infinite families of generalized PBAs are constructed. Expand
Some results on weighing matrices
It is shown that if q is a prime power then there exists a circulant weighing matrix of order q 2 + q + 1 with q 2 nonzero elements per row and column. This result allows the bound N to be lowered inExpand
A note on balanced weighing matrices
A balanced weighing matrix is a square orthogonal matrix of 0’s, 1’s and −1’s such that the matrix obtained by squaring entries is the incidence matrix of a (v, k, λ) configuration. Properties ofExpand
Ternary sequences with perfect periodic autocorrelation
It is shown that the peak factor of radiation is (q 2l+1-1) /(q 2+l-q^{2l}-q2l}) , which is close to 1 as q becomes large. Expand
Infinite families of perfect binary arrays
The author constructs four infinite families of perfect binary arrays. Jedwab and Mitchell have constructed some small perfect binary arrays using quasiperfect binary arrays and doubly quasiperfectExpand
Constructing new perfect binary arrays
Only a small number of different sizes are known for which there exist two-dimensional perfect binary arrays. Construction methods are given which generate new two-dimensional perfect binary arrays,Expand
On the Nonexistence of a Class of Circulant Balanced Weighing Matrices
A balanced weighing matrix is the incidence matrix of a symmetrical balanced incomplete block design (SBIBD) in which some of the “ones” are replaced by “negative ones” in order to obtain anExpand
Some Infinite Classes of Special Williamson Matrices and Difference Sets
  • Ming-Yuan Xia
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
  • 1992
There exist Hadamard matrices of special Williamson kind and difference sets of order 4 × 32r × (p1r1···pnrn)4 for any integer n ⩾ 1, primes p1, …, pn, and all nonnegative integers r, r1,…, rn. Expand
New Constructions of Menon Difference Sets
This paper provides a construction of difference sets in higher exponent groups, and this provides new examples of perfect binary arrays. Expand