Construction of T-matrices of order 6m + 1

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Far East Journal of Mathematical Sciences, ISSN: 0972-0871, Vol: 101, Issue: 8, Page: 1731-1749

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Xia, Mingyuan; Xia, Tianbing; Seberry, Jennifer; Qin, Hong
Pushpa Publishing House
Mathematics; construction; 6m+1; t-matrices; order
article description
In this paper, we prove the necessary and sufficient condition for an integer n to equal a+ 3b. Consequently, every prime power 6m + 1 has a representation of the form a+ 3b. Then we show how to construct T-matrices of order 6m + 1 by using 4 sequences of lengths r, r, 2m − r, 2m − r with r = m − 2 or r = m in which the first is a subset of the integers {0, 1, …, 2m − 1} with size r, the second and third sequences are of (1, −1), and every component of the last sequence belongs to the set {0, 1, 2}. For m ≤ 13 and m ≠ 9, we give concrete constructions.