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Existence of APAV(q, k) with q a prime power ≡ 3 (mod 4) and k odd > 1

✍ Scribed by K. Chen; L. Zhu

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 216 KB
Volume: 7
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1999)7:1<57::aid-jcd7>3.0.co;2-4

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✦ Synopsis

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. In this article, we use a theorem on character sums to show that for any prime power q ≡ 3 (mod 4) and any odd k > 1 such a vector exists whenever q > (

2 . In particular, we determine the existence of an APAV(q, k) with a prime power q ≡ 3 (mod 4) and k = 7, 9, 11, 13, 15.

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