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

✍ Scribed by Kejun Chen; Zhenfu Cao; Dianhua Wu

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
214 KB
Volume
279
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

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. 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]2 5m -3, F = m(2m + 1)(k -3)2 5m and m = (k -1)=4.

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