On the rectangularity of nonlinear block codes

Vladimir Sidorenko; Lan Martin; Bahram Honary

doi:10.1109/18.749021

On the rectangularity of nonlinear block codes

Vladimir Sidorenko
, Lan Martin
, Bahram Honary

Institute for Information Transmission Problems of the Russian Academy of Sciences

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

2 Scopus citations

Abstract

We give simple sufficient conditions for a code to be rectangular and show that large families of well-known nonlinear codes are rectangular. These include Hadamard, Levenshtein, Delsarte-Goethals, Kerdock, and Nordstrom-Robinson codes. Being rectangular, each of these codes has a unique minimal trellis that can be used for soft-decision maximum-likelihood decoding.

Original language	English
Pages (from-to)	720-725
Number of pages	6
Journal	IEEE Transactions on Information Theory
Volume	45
Issue number	2
DOIs	https://doi.org/10.1109/18.749021
State	Published - 1999
Externally published	Yes

Keywords

Codes
Delsarte-goethals
Hadamard
Kerdock
Levenshtein
Nonlinear
Nordstrom-robinson
Rectangular
Trellis

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10.1109/18.749021

Cite this

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title = "On the rectangularity of nonlinear block codes",

abstract = "We give simple sufficient conditions for a code to be rectangular and show that large families of well-known nonlinear codes are rectangular. These include Hadamard, Levenshtein, Delsarte-Goethals, Kerdock, and Nordstrom-Robinson codes. Being rectangular, each of these codes has a unique minimal trellis that can be used for soft-decision maximum-likelihood decoding.",

keywords = "Codes, Delsarte-goethals, Hadamard, Kerdock, Levenshtein, Nonlinear, Nordstrom-robinson, Rectangular, Trellis",

author = "Vladimir Sidorenko and Lan Martin and Bahram Honary",

note = "Funding Information: Manuscript received October 20, 1996; revised March 5, 1998. This work was supported in part by the Royal Society, U.K. V. Sidorenko is with the Institute for Problems of Information Transmission, Russian Academy of Science, Moscow GSP-4, Russia. I. Martin and B. Honary are with the Communications Research Centre, Lancaster University, Lancaster LA1 4YR, U.K. Communicated by A. Vardy, Associate Editor for Coding Theory. Publisher Item Identifier S 0018-9448(99)01409-1.",

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doi = "10.1109/18.749021",

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T1 - On the rectangularity of nonlinear block codes

AU - Sidorenko, Vladimir

AU - Martin, Lan

AU - Honary, Bahram

N1 - Funding Information: Manuscript received October 20, 1996; revised March 5, 1998. This work was supported in part by the Royal Society, U.K. V. Sidorenko is with the Institute for Problems of Information Transmission, Russian Academy of Science, Moscow GSP-4, Russia. I. Martin and B. Honary are with the Communications Research Centre, Lancaster University, Lancaster LA1 4YR, U.K. Communicated by A. Vardy, Associate Editor for Coding Theory. Publisher Item Identifier S 0018-9448(99)01409-1.

PY - 1999

Y1 - 1999

N2 - We give simple sufficient conditions for a code to be rectangular and show that large families of well-known nonlinear codes are rectangular. These include Hadamard, Levenshtein, Delsarte-Goethals, Kerdock, and Nordstrom-Robinson codes. Being rectangular, each of these codes has a unique minimal trellis that can be used for soft-decision maximum-likelihood decoding.

AB - We give simple sufficient conditions for a code to be rectangular and show that large families of well-known nonlinear codes are rectangular. These include Hadamard, Levenshtein, Delsarte-Goethals, Kerdock, and Nordstrom-Robinson codes. Being rectangular, each of these codes has a unique minimal trellis that can be used for soft-decision maximum-likelihood decoding.

KW - Codes

KW - Delsarte-goethals

KW - Hadamard

KW - Kerdock

KW - Levenshtein

KW - Nonlinear

KW - Nordstrom-robinson

KW - Rectangular

KW - Trellis

UR - https://www.scopus.com/pages/publications/0033100442

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DO - 10.1109/18.749021

M3 - Article

AN - SCOPUS:0033100442

SN - 0018-9448

VL - 45

SP - 720

EP - 725

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 2

ER -

On the rectangularity of nonlinear block codes

Abstract

Keywords

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