A recursive definition of p -ary addition without carry

François Laubie

Journal de théorie des nombres de Bordeaux (1999)

  • Volume: 11, Issue: 2, page 307-315
  • ISSN: 1246-7405

Abstract

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Let p be a prime number. In this paper we prove that the addition in p -ary without carry admits a recursive definition like in the already known cases p = 2 and p = 3 .

How to cite

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Laubie, François. "A recursive definition of $p$-ary addition without carry." Journal de théorie des nombres de Bordeaux 11.2 (1999): 307-315. <http://eudml.org/doc/248328>.

@article{Laubie1999,
abstract = {Let $p$ be a prime number. In this paper we prove that the addition in $p$-ary without carry admits a recursive definition like in the already known cases $p = 2$ and $p = 3$.},
author = {Laubie, François},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {-ary representations of integers},
language = {eng},
number = {2},
pages = {307-315},
publisher = {Université Bordeaux I},
title = {A recursive definition of $p$-ary addition without carry},
url = {http://eudml.org/doc/248328},
volume = {11},
year = {1999},
}

TY - JOUR
AU - Laubie, François
TI - A recursive definition of $p$-ary addition without carry
JO - Journal de théorie des nombres de Bordeaux
PY - 1999
PB - Université Bordeaux I
VL - 11
IS - 2
SP - 307
EP - 315
AB - Let $p$ be a prime number. In this paper we prove that the addition in $p$-ary without carry admits a recursive definition like in the already known cases $p = 2$ and $p = 3$.
LA - eng
KW - -ary representations of integers
UR - http://eudml.org/doc/248328
ER -

References

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  2. [2] J.H. Conway, N.J.A. Sloane, Lexicographic Codes, Error Corrrecting Codes from Game Theory. IEEE Trans. Inform. Theory32 (1986), 337-348. Zbl0594.94023MR838197
  3. [3] S. Eliahou, M. Kervaire, Sumsets in vector spaces over finite fields. J. Number Theory71 (1998), 12-39. Zbl0935.11003MR1631038
  4. [4] F. Laubie, On linear greedy codes. to appear. 
  5. [5] H.W. Lenstra, Nim Multiplication. Séminaire de Théorie des Nombres de Bordeaux 1977-78, exposé 11, (1978). Zbl0395.90119MR550271
  6. [6] V. Levenstein, A class of Systematic Codes. Soviet Math Dokl.1 (1960), 368-371. Zbl0095.11503MR122629
  7. [7] S.Y.R. Li, N-person Nim and N-person Moore's Games. Int. J. Game Theory7 (1978), 31-36. Zbl0382.90101MR484458
  8. [8] E.H. Moore, A generalization of the Game called Nim. Ann. Math. Princeton11 (1910), 93-94. Zbl41.0263.02MR1502397JFM41.0263.02

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