Power-Properties of Codes

Tetsuo MORIYA

Power-Properties of Codes

Tetsuo MORIYA

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We consider the following three statements for a code L. (P1) For every n 2, both wⁿ Lⁿ and wⁿ⁺¹ Lⁿ⁺¹ imply w L. (P2) For every n 2, if wⁿ Lⁿ, then w L. (P3) For every m, k 2 with m k, w^k L^m implies w L. First we show that for every code L, P1 holds. Next we show that for every infix code L, P2 holds, and that a code L is an infix code iff P2 holds and L is a weakly infix code. Last we show that for every strongly infix code L, P3 holds, and that a code L is a strongly infix code iff P3 holds and L is a hyper infix code.

Publication: IEICE TRANSACTIONS on Information Vol.E85-D No.3 pp.577-579

Publication Date: 2002/03/01

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Type of Manuscript: LETTER

Category: Theory of Automata, Formal Language Theory

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Tetsuo MORIYA, "Power-Properties of Codes" in IEICE TRANSACTIONS on Information, vol. E85-D, no. 3, pp. 577-579, March 2002, doi: .
Abstract: We consider the following three statements for a code L. (P1) For every n 2, both wⁿ Lⁿ and wⁿ⁺¹ Lⁿ⁺¹ imply w L. (P2) For every n 2, if wⁿ Lⁿ, then w L. (P3) For every m, k 2 with m k, w^k L^m implies w L. First we show that for every code L, P1 holds. Next we show that for every infix code L, P2 holds, and that a code L is an infix code iff P2 holds and L is a weakly infix code. Last we show that for every strongly infix code L, P3 holds, and that a code L is a strongly infix code iff P3 holds and L is a hyper infix code.
URL: https://global.ieice.org/en_transactions/information/10.1587/e85-d_3_577/_p

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@ARTICLE{e85-d_3_577,
author={Tetsuo MORIYA, },
journal={IEICE TRANSACTIONS on Information},
title={Power-Properties of Codes},
year={2002},
volume={E85-D},
number={3},
pages={577-579},
abstract={We consider the following three statements for a code L. (P1) For every n 2, both wⁿ Lⁿ and wⁿ⁺¹ Lⁿ⁺¹ imply w L. (P2) For every n 2, if wⁿ Lⁿ, then w L. (P3) For every m, k 2 with m k, w^k L^m implies w L. First we show that for every code L, P1 holds. Next we show that for every infix code L, P2 holds, and that a code L is an infix code iff P2 holds and L is a weakly infix code. Last we show that for every strongly infix code L, P3 holds, and that a code L is a strongly infix code iff P3 holds and L is a hyper infix code.},
keywords={},
doi={},
ISSN={},
month={March},}

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TY - JOUR
TI - Power-Properties of Codes
T2 - IEICE TRANSACTIONS on Information
SP - 577
EP - 579
AU - Tetsuo MORIYA
PY - 2002
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E85-D
IS - 3
JA - IEICE TRANSACTIONS on Information
Y1 - March 2002
AB - We consider the following three statements for a code L. (P1) For every n 2, both wⁿ Lⁿ and wⁿ⁺¹ Lⁿ⁺¹ imply w L. (P2) For every n 2, if wⁿ Lⁿ, then w L. (P3) For every m, k 2 with m k, w^k L^m implies w L. First we show that for every code L, P1 holds. Next we show that for every infix code L, P2 holds, and that a code L is an infix code iff P2 holds and L is a weakly infix code. Last we show that for every strongly infix code L, P3 holds, and that a code L is a strongly infix code iff P3 holds and L is a hyper infix code.
ER -