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Definition
The minimal polynomial of a linear recurring sequence \(\mathbf{ s} = {({s}_{t})}_{t\geq 0}\) of elements of \({\mathbf F}_{q}\) is the polynomial \(P\) in \({\mathbf F}_{q}[X]\) of lowest degree such that \({({s}_{t})}_{t\geq 0}\) is generated by the linear feedback shift register (LFSR) with characteristic polynomial \(P\). In other terms, \(P ={ \sum \nolimits }_{i=0}^{L-1}{p}_{i}{X}^{i} + {X}^{L}\) is the characteristic polynomial of the linear recurrence relation of least degree satisfied by the sequence:
The minimal polynomial of a linear recurring sequence s is monic and unique; it divides the characteristic polynomial of any LFSR which generates s. The degree of the minimal polynomial of s is called its linear complexity. The period of the minimal polynomial of sis equal to the least...
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Canteaut, A. (2011). Minimal Polynomial. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_360
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DOI: https://doi.org/10.1007/978-1-4419-5906-5_360
Publisher Name: Springer, Boston, MA
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