Linear Complexity of Periodic Sequences Obtained from a Sequence over GF(p) with Period pn-1 by One-Symbol Deletion

Satoshi UEHARA; Kyoki IMAMURA

Linear Complexity of Periodic Sequences Obtained from a Sequence over GF(p) with Period pⁿ-1 by One-Symbol Deletion

Satoshi UEHARA, Kyoki IMAMURA

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From a sequence {a_i}_i0 over GF(p) with period pⁿ-1 we can obtain another periodic sequence {_i}_i0 with period pⁿ-2 by deleting one symbol at the end of each period. We will give the bounds (upper bound and lower bound) of linear complexity of {_i}_i0 as a typical example of instability of linear complexity. Derivation of the bounds are performed by using the relation of characteristic polynomials between {a_i}_i0 and {a_i(j)}_i0={a_i+j}_i0, jGF(p){0}. For a binary m-sequence {a_i}_i0 with period 2ⁿ-1, n-1 a prime, we will give the explicit formula for the characteristic polynomial of {_i}_i0.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E80-A No.6 pp.1164-1166

Publication Date: 1997/06/25

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Category: Information Theory and Coding Theory

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Satoshi UEHARA, Kyoki IMAMURA, "Linear Complexity of Periodic Sequences Obtained from a Sequence over GF(p) with Period pn-1 by One-Symbol Deletion" in IEICE TRANSACTIONS on Fundamentals, vol. E80-A, no. 6, pp. 1164-1166, June 1997, doi: .
Abstract: From a sequence {a_i}_i0 over GF(p) with period pⁿ-1 we can obtain another periodic sequence {_i}_i0 with period pⁿ-2 by deleting one symbol at the end of each period. We will give the bounds (upper bound and lower bound) of linear complexity of {_i}_i0 as a typical example of instability of linear complexity. Derivation of the bounds are performed by using the relation of characteristic polynomials between {a_i}_i0 and {a_i(j)}_i0={a_i+j}_i0, jGF(p){0}. For a binary m-sequence {a_i}_i0 with period 2ⁿ-1, n-1 a prime, we will give the explicit formula for the characteristic polynomial of {_i}_i0.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e80-a_6_1164/_p

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@ARTICLE{e80-a_6_1164,
author={Satoshi UEHARA, Kyoki IMAMURA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Linear Complexity of Periodic Sequences Obtained from a Sequence over GF(p) with Period pn-1 by One-Symbol Deletion},
year={1997},
volume={E80-A},
number={6},
pages={1164-1166},
abstract={From a sequence {a_i}_i0 over GF(p) with period pⁿ-1 we can obtain another periodic sequence {_i}_i0 with period pⁿ-2 by deleting one symbol at the end of each period. We will give the bounds (upper bound and lower bound) of linear complexity of {_i}_i0 as a typical example of instability of linear complexity. Derivation of the bounds are performed by using the relation of characteristic polynomials between {a_i}_i0 and {a_i(j)}_i0={a_i+j}_i0, jGF(p){0}. For a binary m-sequence {a_i}_i0 with period 2ⁿ-1, n-1 a prime, we will give the explicit formula for the characteristic polynomial of {_i}_i0.},
keywords={},
doi={},
ISSN={},
month={June},}

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TY - JOUR
TI - Linear Complexity of Periodic Sequences Obtained from a Sequence over GF(p) with Period pn-1 by One-Symbol Deletion
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1164
EP - 1166
AU - Satoshi UEHARA
AU - Kyoki IMAMURA
PY - 1997
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E80-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 1997
AB - From a sequence {a_i}_i0 over GF(p) with period pⁿ-1 we can obtain another periodic sequence {_i}_i0 with period pⁿ-2 by deleting one symbol at the end of each period. We will give the bounds (upper bound and lower bound) of linear complexity of {_i}_i0 as a typical example of instability of linear complexity. Derivation of the bounds are performed by using the relation of characteristic polynomials between {a_i}_i0 and {a_i(j)}_i0={a_i+j}_i0, jGF(p){0}. For a binary m-sequence {a_i}_i0 with period 2ⁿ-1, n-1 a prime, we will give the explicit formula for the characteristic polynomial of {_i}_i0.
ER -

Linear Complexity of Periodic Sequences Obtained from a Sequence over GF(p) with Period pⁿ-1 by One-Symbol Deletion

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