On the nonexistence of perfect 2- and 3-Hamming-error-correcting codes over GF(q)

J.H. van Lint

On the nonexistence of perfect 2- and 3-Hamming-error-correcting codes over GF(q)

J.H. van Lint

Mathematics and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic

11 Citations (Scopus)

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Abstract

Abstract only given, substantially as follows. Let p be a prime, q=p/sup a/, F=GF(q) and let V be the vectorspace F/sup N/. For any x epsilon V weight of x is defined to be the number of non-zero components of x. The (Hamming-) distance d(x,y) of 2 vectors x,y of V is defined to be the weight of x-y. If e is a positive integer the sphere B(x,e) is defined by B(x,e):={y epsilon V:d(x,y)

Original language	English
Title of host publication	Program and abstracts of papers to be presented at the 1970 international symposium on information theory (June 15-19, 1970, Noordwijk, The Netherlands)
Place of Publication	New York, NY, USA
Publisher	Institute of Electrical and Electronics Engineers
Pages	1
Publication status	Published - 1970

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title = "On the nonexistence of perfect 2- and 3-Hamming-error-correcting codes over GF(q)",

abstract = "Abstract only given, substantially as follows. Let p be a prime, q=p/sup a/, F=GF(q) and let V be the vectorspace F/sup N/. For any x epsilon V weight of x is defined to be the number of non-zero components of x. The (Hamming-) distance d(x,y) of 2 vectors x,y of V is defined to be the weight of x-y. If e is a positive integer the sphere B(x,e) is defined by B(x,e):={y epsilon V:d(x,y)",

author = "{van Lint}, J.H.",

year = "1970",

language = "English",

pages = "1",

booktitle = "Program and abstracts of papers to be presented at the 1970 international symposium on information theory (June 15-19, 1970, Noordwijk, The Netherlands)",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

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On the nonexistence of perfect 2- and 3-Hamming-error-correcting codes over GF(q). / van Lint, J.H.

Program and abstracts of papers to be presented at the 1970 international symposium on information theory (June 15-19, 1970, Noordwijk, The Netherlands). New York, NY, USA : Institute of Electrical and Electronics Engineers, 1970. p. 1.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic

TY - GEN

T1 - On the nonexistence of perfect 2- and 3-Hamming-error-correcting codes over GF(q)

AU - van Lint, J.H.

PY - 1970

Y1 - 1970

N2 - Abstract only given, substantially as follows. Let p be a prime, q=p/sup a/, F=GF(q) and let V be the vectorspace F/sup N/. For any x epsilon V weight of x is defined to be the number of non-zero components of x. The (Hamming-) distance d(x,y) of 2 vectors x,y of V is defined to be the weight of x-y. If e is a positive integer the sphere B(x,e) is defined by B(x,e):={y epsilon V:d(x,y)

AB - Abstract only given, substantially as follows. Let p be a prime, q=p/sup a/, F=GF(q) and let V be the vectorspace F/sup N/. For any x epsilon V weight of x is defined to be the number of non-zero components of x. The (Hamming-) distance d(x,y) of 2 vectors x,y of V is defined to be the weight of x-y. If e is a positive integer the sphere B(x,e) is defined by B(x,e):={y epsilon V:d(x,y)

M3 - Conference contribution

SP - 1

BT - Program and abstracts of papers to be presented at the 1970 international symposium on information theory (June 15-19, 1970, Noordwijk, The Netherlands)

PB - Institute of Electrical and Electronics Engineers

CY - New York, NY, USA

ER -

On the nonexistence of perfect 2- and 3-Hamming-error-correcting codes over GF(q)

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