Linear Complexity of Periodic Sequences Obtained from GF(q) Sequences with Period qn-1 by One-Symbol Insertion

Satoshi UEHARA; Kyoki IMAMURA

IEICE TRANSACTIONS on Fundamentals

Linear Complexity of Periodic Sequences Obtained from GF(q) Sequences with Period qⁿ-1 by One-Symbol Insertion

Satoshi UEHARA, Kyoki IMAMURA

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From a GF(q) sequence {a_i}_i0 with period qⁿ - 1 we can obtain new periodic sequences {a_i}_i0 with period qⁿ by inserting one symbol b GF(q) at the end of each period. Let b₀ = Σqⁿ-2 i=0 a_i. It Is first shown that the linear complexity of {a_i}_i0, denoted as LC({a_i}) satisfies LC({a_i}) = qⁿ if b -b₀ and LC({a_i}) qⁿ - 1 if b = -b₀ Most of known sequences are shown to satisfy the zero sum property, i.e., b₀ = 0. For such sequences satisfying b₀ = 0 it is shown that qⁿ - LC({a_i}) LC({a_i}) qⁿ - 1 if b = 0.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E79-A No.10 pp.1739-1740

Publication Date: 1996/10/25

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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 GF(q) Sequences with Period qn-1 by One-Symbol Insertion" in IEICE TRANSACTIONS on Fundamentals, vol. E79-A, no. 10, pp. 1739-1740, October 1996, doi: .
Abstract: From a GF(q) sequence {a_i}_i0 with period qⁿ - 1 we can obtain new periodic sequences {a_i}_i0 with period qⁿ by inserting one symbol b GF(q) at the end of each period. Let b₀ = Σqⁿ-2 i=0 a_i. It Is first shown that the linear complexity of {a_i}_i0, denoted as LC({a_i}) satisfies LC({a_i}) = qⁿ if b -b₀ and LC({a_i}) qⁿ - 1 if b = -b₀ Most of known sequences are shown to satisfy the zero sum property, i.e., b₀ = 0. For such sequences satisfying b₀ = 0 it is shown that qⁿ - LC({a_i}) LC({a_i}) qⁿ - 1 if b = 0.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e79-a_10_1739/_p

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@ARTICLE{e79-a_10_1739,
author={Satoshi UEHARA, Kyoki IMAMURA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Linear Complexity of Periodic Sequences Obtained from GF(q) Sequences with Period qn-1 by One-Symbol Insertion},
year={1996},
volume={E79-A},
number={10},
pages={1739-1740},
abstract={From a GF(q) sequence {a_i}_i0 with period qⁿ - 1 we can obtain new periodic sequences {a_i}_i0 with period qⁿ by inserting one symbol b GF(q) at the end of each period. Let b₀ = Σqⁿ-2 i=0 a_i. It Is first shown that the linear complexity of {a_i}_i0, denoted as LC({a_i}) satisfies LC({a_i}) = qⁿ if b -b₀ and LC({a_i}) qⁿ - 1 if b = -b₀ Most of known sequences are shown to satisfy the zero sum property, i.e., b₀ = 0. For such sequences satisfying b₀ = 0 it is shown that qⁿ - LC({a_i}) LC({a_i}) qⁿ - 1 if b = 0.},
keywords={},
doi={},
ISSN={},
month={October},}

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TY - JOUR
TI - Linear Complexity of Periodic Sequences Obtained from GF(q) Sequences with Period qn-1 by One-Symbol Insertion
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1739
EP - 1740
AU - Satoshi UEHARA
AU - Kyoki IMAMURA
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E79-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 1996
AB - From a GF(q) sequence {a_i}_i0 with period qⁿ - 1 we can obtain new periodic sequences {a_i}_i0 with period qⁿ by inserting one symbol b GF(q) at the end of each period. Let b₀ = Σqⁿ-2 i=0 a_i. It Is first shown that the linear complexity of {a_i}_i0, denoted as LC({a_i}) satisfies LC({a_i}) = qⁿ if b -b₀ and LC({a_i}) qⁿ - 1 if b = -b₀ Most of known sequences are shown to satisfy the zero sum property, i.e., b₀ = 0. For such sequences satisfying b₀ = 0 it is shown that qⁿ - LC({a_i}) LC({a_i}) qⁿ - 1 if b = 0.
ER -

IEICE TRANSACTIONS on Fundamentals

Linear Complexity of Periodic Sequences Obtained from GF(q) Sequences with Period qⁿ-1 by One-Symbol Insertion

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