Elsevier

Discrete Mathematics

Volume 279, Issues 1–3, 28 March 2004, Pages 153-161
Discrete Mathematics

Existence of APAV(q,k) with q a prime power ≡5(mod8) and k≡1(mod4)

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Abstract

Stinson introduced authentication perpendicular arrays APAλ(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(mod4) and odd k>1. In this article, we show that for any prime power q≡5(mod8) and any k≡1(mod4) there exists an APAV(q,k) whenever q>((E+E2+4F)/2)2, where E=[(7k−23)m+3]25m−3, F=m(2m+1)(k−3)25m and m=(k−1)/4.

Keywords

Perpendicular array
Authentication perpendicular array vector
Finite field
Multiplicative character
Weil's theorem

Cited by (0)

Research supported in part by the National Science Fund for Distinguished Young Scholars (Grant 60225007), the Fund from Postdoctoral Fellowship (Grant 2003033312) and the Fund from Jiangsu Education Commission (Grant 01KJB11006).

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Present address: Department of Mathematics, Yancheng Teachers College, Jiangsu 224002, China.