A proof of maximum contention-free property of interleavers for Turbo codes using permutation polynomials over integer rings

It is well known that interleavers play a critical role in Turbo coding/decoding schemes, and contention-free interleaver design has become a serious problem in the paraUelization of Turbo decoding, which is indispensable to meet the demands for high throughput and low latency in next generation mobile communication systems. This paper unveils the fact that interleavers based on permutation polynomials modulo N are contention-free for every window size W, a factor of the intedeaver length N, which, also called maximum contention-free interleavers.

关于不定方程x^2+64=y^5

讨论了不定方程x2+64=y5,利用代数数论的方法证明了不定方程x2+64=y5无整数解。

INJECTIVE MAPS ON PRIMITIVE SEQUENCES OVER Z/(p^e)

Let Z/（p^e） be the integer residue ring modulo p^e with p an odd prime and integer e ≥ 3. For a sequence a over Z/（p^e）, there is a unique p-adic decomposition a- = a-0 ＋a-1 .p ＋… ＋ a-e-l .p^e-1 where each a-i can be regarded as a sequence over Z/（p）, 0 ≤ i ≤ e - 1. Let f（x） be a primitive polynomial over Z/（p^e） and G＇（f（x）,p^e） the set of all primitive sequences generated by f（x） over Z/（p^e）. For μ（x） ∈ Z/（p）[x] with deg（μ（x）） ≥ 2 and gad（1 ＋ deg（μ（x））,p- 1） = 1, setφe-1 （x0, x1,… , xe-1） = xe-1. [μ（xe-2） ＋ ηe-3（x0, X1,…, xe-3）] ＋ ηe-2（x0, X1,…, xe-2） which is a function of e variables over Z/（p）. Then the compressing mapφe-1 ： G＇（f（x）,p^e） → （Z/（p））^∞ ,a-→φe-1（a-0,a-1, … ,a-e-1） is injective. That is, for a-,b-∈ G＇（f（x）,p^e）, a- = b- if and only if φe-1 （a-0,a-1, … ,a-e-1） = φe-1（b-0, b-1,… ,b-e-1）. As for the case of e = 2, similar result is also given. Furthermore, if functions φe-1 and ψe-1 over Z/（p） are both of the above form and satisfy φe-1（a-0,a-1,…,a-e-1）=ψe-1（b-0, b-1,… ,b-e-1） for a-,b-∈G＇（f（x）,p^e）, the relations between a- and b-, φe-1 and ψe-1 are discussed

An Additive Function on a Ring of Integers in the Imaginary Quadratic Field Q(d^(1/2))with Class-Number One

Let Bα（α）be an additive function on a ring of integers in the quadratic number field Q（（1/2）d）given by Bα（α）=∑p丨α*Nα（p）with a fixed α】0,where the asterisk means that the summation is over the non-associate prime divisors p of an integer α in Q（（1/2）d）,N（α）is the norm of α.In this paper we obtain the asymptotic formula of ∑N（α）≤x *Bα（α）in the case where the class-number of Q（（1/2）d）is one.

The p-adic Approach to Wolstenholme's Theorem

In this note, the authors give a new generalization of the Walstenholme's theorem by using the p-adic approach.

A proactive secret sharing scheme based on Chinese remainder theorem

If an adversary tries to obtain a secret s in a(t,n)threshold secret sharing(SS)scheme,it has to capture no less than t shares instead of the secret s directly.However,if a shareholder keeps a fixed share for a long time,an adversary may have chances to filch some shareholders’shares.In a proactive secret sharing(PSS)scheme,shareholders are supposed to refresh shares at fixed period without changing the secret.In this way,an adversary can recover the secret if and only if it captures at least t shares during a period rather than any time,and thus PSS provides enhanced protection to long-lived secrets.The existing PSS schemes are almost based on linear SS but no Chinese Remainder Theorem(CRT)-based PSS scheme was proposed.This paper proposes a PSS scheme based on CRT for integer ring to analyze the reason why traditional CRT-based SS is not suitable to design PSS schemes.Then,an ideal PSS scheme based on CRT for polynomial ring is also proposed.The scheme utilizes isomorphism of CRT to implement efficient share refreshing.

Strongly Clean Matrices over Commutative Domains

We get criteria of strong cleanness for several classes of 2 × 2 matrices over integers. For commutative local domains, we establish ones in terms of solvability of quadratic equations. Strongly clean matrices over power series are also studied.