TY - JOUR
T1 - Existence of APAV(q,k) with q a prime power ≡ 5 (mod 8) and k ≡ 1 (mod 4)
AU - Chen, Kejun
AU - Cao, Zhenfu
AU - Wu, Dianhua
PY - 2004/3/28
Y1 - 2004/3/28
N2 - Stinson introduced authentication perpendicular arrays APA λ(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. In this article, we show that for any prime power q ≡ 5(mod 8) and any k≡1(mod 4) there exists an APAV(q,k) whenever q > ((E + √E 2 + 4F)/2)2, where E = [(7k - 23)m + 3]25m - 3, F = m(2m + 1)(k - 3)25m and m = (k - 1)/4.
AB - Stinson introduced authentication perpendicular arrays APA λ(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. In this article, we show that for any prime power q ≡ 5(mod 8) and any k≡1(mod 4) there exists an APAV(q,k) whenever q > ((E + √E 2 + 4F)/2)2, where E = [(7k - 23)m + 3]25m - 3, F = m(2m + 1)(k - 3)25m and m = (k - 1)/4.
KW - Authentication perpendicular array vector
KW - Finite field
KW - Multiplicative character
KW - Perpendicular array
KW - Weil's theorem
UR - https://www.scopus.com/pages/publications/1342308412
U2 - 10.1016/S0012-365X(03)00265-6
DO - 10.1016/S0012-365X(03)00265-6
M3 - 文章
AN - SCOPUS:1342308412
SN - 0012-365X
VL - 279
SP - 153
EP - 161
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 1-3
ER -