Nonexistence of certain perfect arrays

✍ Scribed by Wai-Kiu Chan; Man-Keung Siu; Siu-Lun Ma

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 447 KB
• Volume: 125
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(94)90150-3

✦ Synopsis

Perfect binary arrays are equivalent to Menon difference sets in certain groups. This note proves a theorem on the Menon difference set and interprets its consequences on the nonexistence of certain perfect arrays. examples of perfect arrays of sizes 6 x 6 and 3 x 12. In recent years quite a number of authors working in communication science obtain further and related results, while several authors working in difference sets obtain results which can be adapted to Z, x Z, to yield results on perfect arrays. A survey on these known results can be found in [6]. Readers are referred to its bibliography. (More recent results can be found in Cl09 181.)

Let us agree to exclude from our discussion perfect s x t arrays with s, t relatively prime, which are actually equivalent to perfect sequences or to Menon difference sets