On the trellis representation of the delsarte-goethals codes

Yaron Shany; Ilan Reuven; Yair Be'Ery

doi:10.1109/18.681330

On the trellis representation of the delsarte-goethals codes

Yaron Shany^*
, Ilan Reuven
, Yair Be'Ery

^*Corresponding author for this work

School of Electrical Engineering

Tel Aviv University

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

6 Scopus citations

Abstract

In this correspondence, the trellis representation of the Kerdock and Delsarte-Goethals codes is addressed. It is shown that the states of a trellis representation of DG(m, δ) under any bit-order are either strict-sense nonmerging or strict-sense nonexpanding, except, maybe, at indices within the code's distance set. For δ > 3 and for m > δ, the state complexity, s_max[DG(m, δ)], is found. For all values of m and δ, a formula for the number of states and branches of the biproper trellis diagram of DG(m, δ) is given for some of the indices, and upper and lower bounds are given for the remaining indices. The formula and the bounds refer to the Delsarte-Goethals codes when arranged in the standard bit-order.

Original language	English
Pages (from-to)	1547-1554
Number of pages	8
Journal	IEEE Transactions on Information Theory
Volume	44
Issue number	4
DOIs	https://doi.org/10.1109/18.681330
State	Published - 1998

Keywords

Biproper trellis
Delsarte-Goethals code
Kerdock code
Rectangular codes
Trellis complexity. © 1998 ieee publisher item identifier s 0018-9448(98)03481-6

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10.1109/18.681330

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title = "On the trellis representation of the delsarte-goethals codes",

abstract = "In this correspondence, the trellis representation of the Kerdock and Delsarte-Goethals codes is addressed. It is shown that the states of a trellis representation of DG(m, δ) under any bit-order are either strict-sense nonmerging or strict-sense nonexpanding, except, maybe, at indices within the code's distance set. For δ > 3 and for m > δ, the state complexity, smax[DG(m, δ)], is found. For all values of m and δ, a formula for the number of states and branches of the biproper trellis diagram of DG(m, δ) is given for some of the indices, and upper and lower bounds are given for the remaining indices. The formula and the bounds refer to the Delsarte-Goethals codes when arranged in the standard bit-order.",

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AB - In this correspondence, the trellis representation of the Kerdock and Delsarte-Goethals codes is addressed. It is shown that the states of a trellis representation of DG(m, δ) under any bit-order are either strict-sense nonmerging or strict-sense nonexpanding, except, maybe, at indices within the code's distance set. For δ > 3 and for m > δ, the state complexity, smax[DG(m, δ)], is found. For all values of m and δ, a formula for the number of states and branches of the biproper trellis diagram of DG(m, δ) is given for some of the indices, and upper and lower bounds are given for the remaining indices. The formula and the bounds refer to the Delsarte-Goethals codes when arranged in the standard bit-order.

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On the trellis representation of the delsarte-goethals codes

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