A new class of codes meeting the Griesmer bound

H.C.A. Tilborg, van; T. Helleseth

doi:10.1109/TIT.1981.1056405

A new class of codes meeting the Griesmer bound

H.C.A. Tilborg, van
, T. Helleseth

Discrete Mathematics

Research output: Contribution to journal › Article › Academic › peer-review

22 Citations (Scopus)

Abstract

An infinite sequence ofk-dimensional binary linear block codes is constructed with parametersn=2^{k}+2^{k-2}-15,d=2^{k-1}+2^{k-3}-8,k geq 7. Fork geq 8these codes are unique, while there are five nonisomorphic codes fork=7. By shortening these codes in an appropriate way, one finds codes meeting the Griesmer bound for2^{k-1}+2^{k-3}-15 leq d leq 2^{k-1}+2^{k-3}-8; k geq 7.

Original language	English
Pages (from-to)	548-555
Number of pages	8
Journal	IEEE Transactions on Information Theory
Volume	27
Issue number	5
DOIs	https://doi.org/10.1109/TIT.1981.1056405
Publication status	Published - 1981

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title = "A new class of codes meeting the Griesmer bound",

abstract = "An infinite sequence ofk-dimensional binary linear block codes is constructed with parametersn=2\textasciicircum{}\{k\}+2\textasciicircum{}\{k-2\}-15,d=2\textasciicircum{}\{k-1\}+2\textasciicircum{}\{k-3\}-8,k geq 7. Fork geq 8these codes are unique, while there are five nonisomorphic codes fork=7. By shortening these codes in an appropriate way, one finds codes meeting the Griesmer bound for2\textasciicircum{}\{k-1\}+2\textasciicircum{}\{k-3\}-15 leq d leq 2\textasciicircum{}\{k-1\}+2\textasciicircum{}\{k-3\}-8; k geq 7.",

author = "\{Tilborg, van\}, H.C.A. and T. Helleseth",

year = "1981",

doi = "10.1109/TIT.1981.1056405",

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journal = "IEEE Transactions on Information Theory",

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T1 - A new class of codes meeting the Griesmer bound

AU - Tilborg, van, H.C.A.

AU - Helleseth, T.

PY - 1981

Y1 - 1981

N2 - An infinite sequence ofk-dimensional binary linear block codes is constructed with parametersn=2^{k}+2^{k-2}-15,d=2^{k-1}+2^{k-3}-8,k geq 7. Fork geq 8these codes are unique, while there are five nonisomorphic codes fork=7. By shortening these codes in an appropriate way, one finds codes meeting the Griesmer bound for2^{k-1}+2^{k-3}-15 leq d leq 2^{k-1}+2^{k-3}-8; k geq 7.

AB - An infinite sequence ofk-dimensional binary linear block codes is constructed with parametersn=2^{k}+2^{k-2}-15,d=2^{k-1}+2^{k-3}-8,k geq 7. Fork geq 8these codes are unique, while there are five nonisomorphic codes fork=7. By shortening these codes in an appropriate way, one finds codes meeting the Griesmer bound for2^{k-1}+2^{k-3}-15 leq d leq 2^{k-1}+2^{k-3}-8; k geq 7.

U2 - 10.1109/TIT.1981.1056405

DO - 10.1109/TIT.1981.1056405

M3 - Article

SN - 0018-9448

VL - 27

SP - 548

EP - 555

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 5

ER -

A new class of codes meeting the Griesmer bound

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