The maximum cardinality of trifferent codes with lengths 5 and 6

Stefano Della Fiore; Alessandro Gnutti; Sven C. Polak

doi:10.1016/j.exco.2022.100051

The maximum cardinality of trifferent codes with lengths 5 and 6

Stefano Della Fiore, Alessandro Gnutti, Sven C. Polak

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Abstract

A code  ⊆ {0, 1, 2}𝑛
is said to be trifferent with length 𝑛 when for any three distinct elements of  there exists
a coordinate in which they all differ. Defining  (𝑛) as the maximum cardinality of trifferent codes with length
𝑛,  (𝑛) is unknown for 𝑛 ≥ 5. In this note, we use an optimized search algorithm to show that  (5) = 10 and
 (6) = 13.

Original language	English
Article number	100051
Journal	Examples and Counterexamples
Volume	2
DOIs	https://doi.org/10.1016/j.exco.2022.100051
Publication status	Published - 2022
Externally published	Yes

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1-s2.0-S2666657X22000039-mainFinal published version, 354 KBLicence: CC BY

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title = "The maximum cardinality of trifferent codes with lengths 5 and 6",

abstract = "A code  ⊆ {0, 1, 2}𝑛is said to be trifferent with length 𝑛 when for any three distinct elements of  there existsa coordinate in which they all differ. Defining  (𝑛) as the maximum cardinality of trifferent codes with length𝑛,  (𝑛) is unknown for 𝑛 ≥ 5. In this note, we use an optimized search algorithm to show that  (5) = 10 and (6) = 13.",

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doi = "10.1016/j.exco.2022.100051",

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journal = "Examples and Counterexamples",

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T1 - The maximum cardinality of trifferent codes with lengths 5 and 6

AU - Fiore, Stefano Della

AU - Gnutti, Alessandro

AU - Polak, Sven C.

N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2022

Y1 - 2022

N2 - A code  ⊆ {0, 1, 2}𝑛is said to be trifferent with length 𝑛 when for any three distinct elements of  there existsa coordinate in which they all differ. Defining  (𝑛) as the maximum cardinality of trifferent codes with length𝑛,  (𝑛) is unknown for 𝑛 ≥ 5. In this note, we use an optimized search algorithm to show that  (5) = 10 and (6) = 13.

AB - A code  ⊆ {0, 1, 2}𝑛is said to be trifferent with length 𝑛 when for any three distinct elements of  there existsa coordinate in which they all differ. Defining  (𝑛) as the maximum cardinality of trifferent codes with length𝑛,  (𝑛) is unknown for 𝑛 ≥ 5. In this note, we use an optimized search algorithm to show that  (5) = 10 and (6) = 13.

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DO - 10.1016/j.exco.2022.100051

M3 - Article

SN - 2666-657X

VL - 2

JO - Examples and Counterexamples

JF - Examples and Counterexamples

M1 - 100051

ER -

The maximum cardinality of trifferent codes with lengths 5 and 6

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