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SCIENCE CHINA Information Sciences
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SCIENCE CHINA Information Sciences, Volume 63 , Issue 11 : 212206(2020) https://doi.org/10.1007/s11432-019-2813-7

Boolean-network-based approach for construction of filter generators

Bowen LI 1,2, Jianquan LU 2,*
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  • ReceivedNov 24, 2019
  • AcceptedFeb 5, 2020
  • PublishedOct 9, 2020
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Abstract


References

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  • Table 1  

    Table 1All relations between ${\rm~PD}_{t}$ and $\{{\rm~HW}(x_{1}(t)\oplus~x_{1}(t+1)),~{\rm~HW}(c_{\beta_{t}}\oplus~c_{\beta_{t+1}}),~{\rm~HW}(x_{n}(t+1)\oplus~x_{n}(t+2)),~{\rm~HW}(c_{\beta_{t+1}}\oplus~c_{\beta_{t+2}})\}$
    ${\rm~PD}_{t}$ $\{{\rm~HW}(x_{1}(t)\oplus~x_{1}(t+1)),~{\rm~HW}(c_{\beta_{t}}\oplus~c_{\beta_{t+1}}),~{\rm~HW}(x_{n}(t+1)\oplus~x_{n}(t+2)),~{\rm~HW}(c_{\beta_{t+1}}\oplus~c_{\beta_{t+2}})\}$
    $-$20, 0, 1, 1
    $-$11, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1
    01, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1
    11, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0
    21, 1, 0, 0
  •   

    Algorithm 1 Determine the values of unnecessary bits in sequence $\mathbbm{a}$

    for $t=0$ to $l-1$

    if both of $a_{t}$ and $a_{t+1}$ are unnecessary bits or one of them is unnecessary bit then

    if $(b_{t}\oplus~b_{t+1})=0$ and $(b_{t+1}\oplus~b_{t+2})=1$ then

    Let $a_{t}$ and $a_{t+1}$ satisfy $a_{t}\oplus~a_{t+1}=0$;

    else

    if $(b_{t}\oplus~b_{t+1})=1$ and $(b_{t+1}\oplus~b_{t+2})=0$ then

    Let $a_{t}$ and $a_{t+1}$ satisfy $a_{t}\oplus~a_{t+1}=1$;

    end if

    end if

    else

    $t=t+1$.

    end if

    end for