Genetic algorithms in coding theory : a table for $A_3(n,d)$

R.J.M. Vaessens; E.H.L. Aarts; J.H. van Lint

Genetic algorithms in coding theory : a table for $A_3(n,d)$

R.J.M. Vaessens, E.H.L. Aarts, J.H. van Lint

Research output: Book/Report › Book › Scientific

Abstract

We consider the problem of finding values of $A_3(n,d)$, i.e. the maximal size of a ternary code of length n and minimum distance d. Our approach is based on a search for good lower bounds and a comparison of these bounds with known upper bounds. Several lower bounds are obtained using a genetic local search algorithm. Other lower bounds are obtained by constructing codes. For those cases in which lower and upper bounds coincide, this yields exact values of $A_3(n,d)$. A table is included containing the known values of the upper and lower bounds for $A_3(n,d)$, with n = 16. For some values of n and d the corresponding codes are given.

Original language	English
Place of Publication	Eindhoven
Publisher	Technische Universiteit Eindhoven
Publication status	Published - 1991
Externally published	Yes

Publication series

Name	Memorandum COSOR

Fingerprint Dive into the research topics of 'Genetic algorithms in coding theory : a table for $A_3(n,d)$'. Together they form a unique fingerprint.

Cite this

Vaessens, R. J. M., Aarts, E. H. L., & van Lint, J. H. (1991). Genetic algorithms in coding theory : a table for $A_3(n,d)$. (Memorandum COSOR). Technische Universiteit Eindhoven.

@book{a3b46ee3600b461897765f325577312d,

title = "Genetic algorithms in coding theory : a table for $A_3(n,d)$",

abstract = "We consider the problem of finding values of $A_3(n,d)$, i.e. the maximal size of a ternary code of length n and minimum distance d. Our approach is based on a search for good lower bounds and a comparison of these bounds with known upper bounds. Several lower bounds are obtained using a genetic local search algorithm. Other lower bounds are obtained by constructing codes. For those cases in which lower and upper bounds coincide, this yields exact values of $A_3(n,d)$. A table is included containing the known values of the upper and lower bounds for $A_3(n,d)$, with n = 16. For some values of n and d the corresponding codes are given.",

author = "R.J.M. Vaessens and E.H.L. Aarts and {van Lint}, J.H.",

year = "1991",

language = "English",

series = "Memorandum COSOR",

publisher = "Technische Universiteit Eindhoven",

}

TY - BOOK

T1 - Genetic algorithms in coding theory : a table for $A_3(n,d)$

AU - Vaessens, R.J.M.

AU - Aarts, E.H.L.

AU - van Lint, J.H.

PY - 1991

Y1 - 1991

N2 - We consider the problem of finding values of $A_3(n,d)$, i.e. the maximal size of a ternary code of length n and minimum distance d. Our approach is based on a search for good lower bounds and a comparison of these bounds with known upper bounds. Several lower bounds are obtained using a genetic local search algorithm. Other lower bounds are obtained by constructing codes. For those cases in which lower and upper bounds coincide, this yields exact values of $A_3(n,d)$. A table is included containing the known values of the upper and lower bounds for $A_3(n,d)$, with n = 16. For some values of n and d the corresponding codes are given.

AB - We consider the problem of finding values of $A_3(n,d)$, i.e. the maximal size of a ternary code of length n and minimum distance d. Our approach is based on a search for good lower bounds and a comparison of these bounds with known upper bounds. Several lower bounds are obtained using a genetic local search algorithm. Other lower bounds are obtained by constructing codes. For those cases in which lower and upper bounds coincide, this yields exact values of $A_3(n,d)$. A table is included containing the known values of the upper and lower bounds for $A_3(n,d)$, with n = 16. For some values of n and d the corresponding codes are given.

M3 - Book

T3 - Memorandum COSOR

BT - Genetic algorithms in coding theory : a table for $A_3(n,d)$

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -