Perfect arithmetic codes

H. W., Jr. Lenstra

Séminaire Delange-Pisot-Poitou. Théorie des nombres (1977-1978)

  • Volume: 19, Issue: 1, page 1-14

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Lenstra, H. W., Jr.. "Perfect arithmetic codes." Séminaire Delange-Pisot-Poitou. Théorie des nombres 19.1 (1977-1978): 1-14. <http://eudml.org/doc/110986>.

@article{Lenstra1977-1978,
author = {Lenstra, H. W., Jr.},
journal = {Séminaire Delange-Pisot-Poitou. Théorie des nombres},
keywords = {Perfect Arithmetic Codes; Negacyclic Code},
language = {eng},
number = {1},
pages = {1-14},
publisher = {Secrétariat mathématique},
title = {Perfect arithmetic codes},
url = {http://eudml.org/doc/110986},
volume = {19},
year = {1977-1978},
}

TY - JOUR
AU - Lenstra, H. W., Jr.
TI - Perfect arithmetic codes
JO - Séminaire Delange-Pisot-Poitou. Théorie des nombres
PY - 1977-1978
PB - Secrétariat mathématique
VL - 19
IS - 1
SP - 1
EP - 14
LA - eng
KW - Perfect Arithmetic Codes; Negacyclic Code
UR - http://eudml.org/doc/110986
ER -

References

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  1. [1] Bojarinov ( J.M.) and Kabatjanskij ( G.A.). - Perfect arithmetic AN-codes for correcting single errors [in Russian],Probl. Peredači Inform. , t. 12, fasc. 1, 1976, p. 16-23;[in English] Problems of Inform. Transm., t. 12, 1976, p. 10-16. Zbl0356.94015MR424387
  2. [2] Cooke ( G.) and Weinberger ( P.J.). - On the construction of division chains in algebraic number rings, with applications to SL2 , Comm. in Algebra, t. 3, 1975, p. 481-524. Zbl0315.12001MR387251
  3. [3] Goto ( M.). - A note on perfect decimal AN-codes, Inform. and Control, t. 29, 1975, p. 385-387. Zbl0326.94009MR392146
  4. [4] Goto ( M.) and Fukumura ( T.). - Perfect nonbinary AN-codes with distance three, Inform. and Control, t. 27, 1975, p. 336-348. Zbl0298.94015MR366513
  5. [5] Gricenko ( V.M.). - Nonbinary arithmetic correcting codes [in Russian], Probl. Peredači Inform., t. 5, fasc. 4, 1969, p. 19-27 ; [in English] Problems of Inform. Transm., t. 5, 1969, fasc. 4, p. 15-22. Zbl0265.94009MR351616
  6. [6] Hooley ( C.). - On Artin's conjecture, J. für die reine und angew. Math., t. 225, 1967, p. 209-220. Zbl0221.10048MR207630
  7. [7] Iwaniec ( H.). - Primes of the type ϕ(x , y) + A where ϕ is a quadratic form, Acta Arithm., Warszawa, t. 21, 1972, p. 203-234. Zbl0215.35603
  8. [8] Lenstra ( H.W., Jr). - On Artin's conjecture and Euclid's algorithm in global fields, Invent. Math., Berlin, t. 42, 1977, p. 201-224 ; [cf. Artin's conjecture on primes with prescribed primitive roots, Séminaire DelangePisot-Poitou : Théorie des nombres, 18e année, 1976/77, n° 14, 8 p.]. Zbl0362.12012MR480413
  9. [9] Massey ( J.H.) and Garcia ( O.N.). - Error-correcting codes in computer arithmetic, Advances Inform. Syst. Sc., t. 4, 1972, p. 273-326. Zbl0256.94019
  10. [10] Narkiewicz ( W.). - Elementary and analytic theory of algebraic numbers. - Warszawa, PWN-Polish scientific Publishers, 1974 (Polska Akademia Nauk. Monografie Matematyczne, 57). Zbl0276.12002MR347767
  11. [11] Peterson ( W.W.) and Weldon ( E.Y., Jr). - Error-correcting codes, 2nd edition. - Cambridge, MIT press, 1972. Zbl0251.94007MR347444
  12. [12] Rao ( T.R.N.). - Error coding for arithmetic processors. - London, Academic Press, 1974 (Electrical Science Series). Zbl0301.94006MR398649
  13. [13] Western ( A.E.) and Miller ( J.C.P.). - Tables of indices and primitive roots. - London, CambridgeUniversity Press, 1968 (Royal Society mathematical Tables, 9). Zbl0175.32501MR246488

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