The number of different true permutation polynomial based interleavers under Zhao and Fan sufficient conditions

Correction to: The number of different true permutation polynomial based interleavers under Zhao and Fan sufficient conditions

“…This means: z 1 = (−q 1 ) (mod p), z 2 = z 3 = · · · = z n = 0 (mod p), ∀ p | N , p > 2. 1 Zhao and Fan sufficient conditions for coefficients q 1 , q 2 , . .…”

“…where 0 ≤ τ k ≤ gcd(k!, N ) − 1 (5) In (5), gcd stands for the greatest common divisor. The expanded form of (5) for n = 5 was given in [1] as…”

“…Thus, as it is shown in Sect. 3 from [1], any PP modulo N is equivalent to a PP having the coefficient of the k degree term q k < N gcd(k!,N ) , ∀k = 2, n. However, for a PP under ZF sufficient conditions this condition is not always valid. We detail below these conditions for a NP of degree three, four, and five.…”

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In the original version of this article [1] unfortunately, there are mistakes in some formulas for determining the number of true different cubic, fourth degree, and fifth degree permutation polynomial based interleavers under Zhao and Fan sufficient conditions. The reason for these mistakes was considering all null polynomials.

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When Is the Number of True Different Permutation Polynomials Equal to 0?

“…By using it, the number of td QPPs and CPPs for every N were obtained. In [8,9], the method from [7] was used to determine the number of td CPPs, fourth-degree PPs (4-PPs), and fifth-degree PPs (5-PPs) under Zhao and Fan (ZF) sufficient conditions given in [10]. In [11], an algorithm to determine the number of td PPs of degrees up to five, based on the Weng and Dong (WD) algorithm from [12], was given.…”