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計算有限域GF(q)上2pn-周期序列的k-錯線性復(fù)雜度及其錯誤序列的算法

牛志華,  孔得宇

牛志華, 孔得宇. 計算有限域GF(q)上2pn-周期序列的k-錯線性復(fù)雜度及其錯誤序列的算法[J]. 電子與信息學(xué)報, 2018, 40(7): 1723-1730. doi: 10.11999/JEIT170972
引用本文: 牛志華, 孔得宇. 計算有限域GF(q)上2pn-周期序列的k-錯線性復(fù)雜度及其錯誤序列的算法[J]. 電子與信息學(xué)報, 2018, 40(7): 1723-1730. doi: 10.11999/JEIT170972
NIU Zhihua, KONG Deyu. Algorithm for Computing the k-error Linear Complexity and the Corresponding Error Sequence of 2pn-periodic Sequences over GF(q)[J]. Journal of Electronics & Information Technology, 2018, 40(7): 1723-1730. doi: 10.11999/JEIT170972
Citation: NIU Zhihua, KONG Deyu. Algorithm for Computing the k-error Linear Complexity and the Corresponding Error Sequence of 2pn-periodic Sequences over GF(q)[J]. Journal of Electronics & Information Technology, 2018, 40(7): 1723-1730. doi: 10.11999/JEIT170972

計算有限域GF(q)上2pn-周期序列的k-錯線性復(fù)雜度及其錯誤序列的算法

doi: 10.11999/JEIT170972 cstr: 32379.14.JEIT170972

  • ①(上海大學(xué)計算機工程與科學(xué)學(xué)院 上海 200444) ②(上海大學(xué)先進研究院 上海 200444)

基金項目: 

上海市自然科學(xué)基金 (16ZR1411200, 17ZR1409800)，國家自然科學(xué)基金(61772022, 61572309, 61462077)

詳細信息
    作者簡介:

    牛志華： 女，1976年生，副教授，研究方向為序列密碼. 孔得宇： 男，1991年生，碩士生，研究方向為序列密碼.

  • 中圖分類號: TN918.1

Algorithm for Computing the k-error Linear Complexity and the Corresponding Error Sequence of 2pn-periodic Sequences over GF(q)

  • NIU Zhihua①②    KONG Deyu①

Funds: 

Shanghai Natural Science Foundation (16ZR1411200, 17ZR1409800), The National Nature Science Foundation of China (61772022, 61572309, 61462077)

  • 摘要: 序列的k-錯線性復(fù)雜度是序列線性復(fù)雜度穩(wěn)定性的重要評價指標(biāo)。在求得一個序列k-錯線性復(fù)雜度的同時，也需要求出是哪些位置的改變導(dǎo)致了序列線性復(fù)雜度的下降。該文提出一個在GF(q)上計算2pn-周期序列s的k-錯線性復(fù)雜度以及對應(yīng)的錯誤序列e的算法，這里p和q是素數(shù)，且q是一個模p2的本原根。該文設(shè)計了一個追蹤代價向量的trace函數(shù)，算法通過trace函數(shù)追蹤最小的代價向量來求出對應(yīng)的錯誤序列e，算法得到的序列e使得(s+e)的線性復(fù)雜度達到k-錯線性復(fù)雜度的值。
    Abstract: The k-error linear complexity of a sequence is a fundamental concept for assessing the stability of the linear complexity. After computing the k-error linear complexity of a sequence, those bits that make the linear complexity reduced also need to be computed. For 2pn-periodic sequence over GF(q) , where p and q are odd primes and q is a primitive root modulo p2, an algorithm is presented, which not only computes the k-error linear complexity of a sequence s but also gets the corresponding error sequence e. A function is designed to trace the vector cost called “trace function”, so the error sequence e can be computed by calling the “trace function”, and the linear complexity of (s+e) reaches the k-error linear complexity of the sequence s.
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出版歷程
  • 收稿日期:  2017-10-20
  • 修回日期:  2018-01-15
  • 刊出日期:  2018-07-19

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