In this letter, some perfect Gaussian integer sequences of period 2m- 1 are proposed based on the trace representations of Legendre sequences, Hall's sextic residue sequences, m-sequences, and Gordon-Mills-Welch (GMW) sequences over the finite field \BBF2m. Moreover, the energy efficiency of these sequences is approximately 1 for sufficiently large m.

Motivated by applications in molecular biology and genotyping, this paper proposes a novel model of group testing for identifying items with real-valued status using nonbinary pooling designs under standard arithmetic observation. The purpose is to learn more information of each item to be tested rather than identify only which ones are defectives as was done in conventional group testing. This paper provides several efficiently decodable nonadaptive strategies for the considered problem. The major tool is a new structure called q-ary additive (w, d)-disjunct matrix, which is related to known structures: 1) the conventional disjunct matrix by Kautz and Singleton 1964 and 2) the SQ-disjunct matrix by Emad and Milenkovic 2012.