Dianhua Wu

A construction for doubly pandiagonal magic squares

In this note, a doubly magic rectangle is introduced to construct a doubly pandiagonal magic square. A product construction for doubly magic rectangles is also presented. Infinite classes of doubly pandiagonal magic squares are then obtained, and an answer to problem 22 of [G. Abe, Unsolved problems on magic squares, Discrete Math. 127 (1994) 3] is given.

Further results on optimal (v,{3 ,k},1,{1/2,1/ 2})-OOCs for k=4,5

Variable-weight optical orthogonal code (OOC) was introduced by Yang for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. Some results on the existence of optimal (v,{3,k},1,{1/2,1/2})-OOCs for k=4,5 were obtained. In this paper, it is proved that there exists an optimal (v,{3,5},1,{1/2,1/2})-OOC for each positive integer v=13(mod26), and v>=39. It is also shown that an optimal (2u,{3,4},1,{1/2,1/2})-OOC exists for any positive integer u whose prime factors are all congruent to 1 modulo 18 and not less than 19.

Good equidistant codes constructed from certain combinatorial designs

An (n,M,d;q) code is called equidistant code if the Hamming distance between any two codewords is d. It was proved that for any equidistant (n,M,d;q) code, d=

Further results on balanced ( n , { 3 , 4 } , Λ a , 1 ) -OOCs

Let W = { w 1 , ? , w r } be an ordering of a set of r integers greater than 1, ? a = ( λ a ( 1 ) , ? , λ a ( r ) ) be an r -tuple of positive integers, λ c be a positive integer, and Q = ( q 1 , ? , q r ) be an r -tuple of positive rational numbers whose sum is 1. In 1996, Yang introduced variable-weight optical orthogonal code ( ( n , W , ? a , λ c , Q ) -OOC) for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. Most existing works on variable-weight optical orthogonal codes assume that λ a ( 1 ) , ? , λ a ( r ) = λ c = 1 . In this paper, new balanced ( n , { 3 , 4 } , ? a , 1 ) -OOCs are constructed, where ? a ? { ( 1 , 2 ) , ( 2 , 1 ) , ( 2 , 2 ) } .

Existence of APAV(q;k) with q a prime power ≡ 5 (mod 8) and k ≡ 1 (mod 4)

Stinson introduced authentication perpendicular arrays APA� (t;k;v), as a special kind of perpendicular arrays, to construct authentication and secrecy codes. Ge and Zhu introduced APAV(q;k) to study APA1(2;k;v) for k = 5, 7. Chen and Zhu determined the existence of APAV(q;k) with q a prime power ≡ 3 (mod 4) and odd k? 1. Inthis article, we show that for any prime power q ≡ 5 (mod 8) and any k ≡ 1 (mod 4) there exists anAPAV( q;k) whenever q? ((E + √ E 2 +4 F)=2) 2 , where E = [(7k − 23)m + 3]2 5m − 3, F = m(2m + 1)(k − 3)2 5m and

New ( q , K , λ ) -ADFs via cyclotomy

The concept of a ( q , k , λ , t ) almost difference family (ADF for short) was introduced by Ding and Yin as a useful generalization of the concept of an almost difference set. Some results had been obtained for the existences of ( q , K , λ ) -ADFs, where K = { k 1 , k 2 , ź , k r } is a set of positive integers. In this note, new cyclic ( q , K , λ ) -ADFs are obtained via cyclotomy.

Bounds and constructions for optimal ( n , { 3 , 5 } , Λ a , 1 , Q ) -OOCs

Let W = { w 1 , w 2 , ? , w r } be an ordering of a set of r integers greater than 1, ? a = ( λ a ( 1 ) , λ a ( 2 ) , ? , λ a ( r ) ) be an r -tuple of positive integers, λ c be a positive integer, and Q = ( q 1 , q 2 , ? , q r ) be an r -tuple of positive rational numbers whose sum is 1. In 1996, Yang introduced variable-weight optical orthogonal code ( ( n , W , ? a , λ c , Q ) -OOC) for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. Some work had been done on the constructions of optimal ( n , { 3 , 4 } , ? a , 1 , Q ) -OOCs with unequal auto- and cross-correlation constraints. In this paper, we focus our main attention on ( n , { 3 , 5 } , ? a , 1 , Q ) -OOCs, where ? a ? { ( 1 , 2 ) , ( 2 , 1 ) , ( 2 , 2 ) } . Tight upper bounds on the maximum code size of an ( n , { 3 , 5 } , ? a , 1 , Q ) -OOC are obtained, and infinite classes of optimal balanced ( n , { 3 , 5 } , ? a , 1 ) -OOCs are constructed.

Bounds and constructions for (v,W,2,Q)-OOCs

Abstract In 1996, Yang introduced variable-weight optical orthogonal code for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. Let W = { w 1 , … , w r } be an ordering of a set of r integers greater than 1 , λ be a positive integer ( auto- and cross-correlation parameter ), and Q = ( q 1 , … , q r ) be an r -tuple ( weight distribution sequence ) of positive rational numbers whose sum is 1 . A ( v , W , λ , Q ) variable-weight optical orthogonal code ( ( v , W , λ , Q ) -OOC) is a collection of ( 0 , 1 ) sequences with weights in W , auto- and cross-correlation parameter λ . Some work has been done on the construction of optimal ( v , W , 1 , Q ) -OOCs, while little is known on the construction of ( v , W , λ , Q ) -OOCs with λ ≥ 2 . It is well known that ( v , W , λ , Q ) -OOCs with λ ≥ 2 have much bigger cardinality than those of ( v , W , 1 , Q ) -OOCs for the same v , W , Q . In this paper, a new upper bound on the number of codewords of ( v , W , λ , Q ) -OOCs is given, and infinite classes of optimal ( v , { 3 , 4 } , 2 , Q ) -OOCs are constructed.