Jacobi polynomials and design theory I

Himadri Shekhar Chakraborty; Tsuyoshi Miezaki; Manabu Oura; Yuuho Tanaka

doi:10.1016/j.disc.2023.113339

Jacobi polynomials and design theory I

Himadri Shekhar Chakraborty, Tsuyoshi Miezaki, Manabu Oura, Yuuho Tanaka^*

^*Corresponding author for this work

School of Fundamental Science and Engineering

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

Abstract

In this paper, we introduce the notion of Jacobi polynomials of a code with multiple reference vectors, and give the MacWilliams type identity for it. Moreover, we derive a formula to obtain the Jacobi polynomials using the Aronhold polarization operator. Finally, we describe some facts obtained from Type III and Type IV codes that interpret the relation between the Jacobi polynomials and designs.

Original language	English
Article number	113339
Journal	Discrete Mathematics
Volume	346
Issue number	6
DOIs	https://doi.org/10.1016/j.disc.2023.113339
Publication status	Published - 2023 Jun

Keywords

Codes
Designs
Invariant theory
Jacobi polynomials

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2023.113339

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title = "Jacobi polynomials and design theory I",

abstract = "In this paper, we introduce the notion of Jacobi polynomials of a code with multiple reference vectors, and give the MacWilliams type identity for it. Moreover, we derive a formula to obtain the Jacobi polynomials using the Aronhold polarization operator. Finally, we describe some facts obtained from Type III and Type IV codes that interpret the relation between the Jacobi polynomials and designs.",

keywords = "Codes, Designs, Invariant theory, Jacobi polynomials",

author = "Chakraborty, {Himadri Shekhar} and Tsuyoshi Miezaki and Manabu Oura and Yuuho Tanaka",

note = "Funding Information: This work was supported by JSPS KAKENHI ( 22K03277 ). Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

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AU - Chakraborty, Himadri Shekhar

AU - Miezaki, Tsuyoshi

AU - Oura, Manabu

AU - Tanaka, Yuuho

PY - 2023/6

Y1 - 2023/6

N2 - In this paper, we introduce the notion of Jacobi polynomials of a code with multiple reference vectors, and give the MacWilliams type identity for it. Moreover, we derive a formula to obtain the Jacobi polynomials using the Aronhold polarization operator. Finally, we describe some facts obtained from Type III and Type IV codes that interpret the relation between the Jacobi polynomials and designs.

AB - In this paper, we introduce the notion of Jacobi polynomials of a code with multiple reference vectors, and give the MacWilliams type identity for it. Moreover, we derive a formula to obtain the Jacobi polynomials using the Aronhold polarization operator. Finally, we describe some facts obtained from Type III and Type IV codes that interpret the relation between the Jacobi polynomials and designs.

KW - Codes

KW - Designs

KW - Invariant theory

KW - Jacobi polynomials

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JO - Discrete Mathematics

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ER -

Jacobi polynomials and design theory I

Abstract

Keywords

ASJC Scopus subject areas

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