New construction of p-ary sequence family with large linear span

In this paper, we propose a method to construct sequence family S_r = {tr₁ ^m ([tr_m ⁿ (alpha^t) + tr_m ⁿ (balpha^dt)]^r) | b isin F_p ⁿ, 0 les t < pⁿ - 1} with large linear span from a sequence family S₁, where gcd(r, p^m - 1) = 1. Let T = (pⁿ - 1)/(p^m - 1). If dT = T mod pⁿ - 1, the correlation distributions of families S_r are the same. Two examples of decimation factor d satisfying the condition dT = T mod pⁿ - 1 are given and the linear span of the ternary sequences in S_r with d = 2p^m - 1 is derived for some cases.