Improved Upper Bound for the Size of a Trifferent Code

Bhandari, S and Khetan, A (2024) Improved Upper Bound for the Size of a Trifferent Code. In: International Symposium on Information Theory, ISIT 2024, 7 July 2024through 12 July 2024, Athens, pp. 1758-1763.

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Abstract

A subset C � 0, 1, 2n is said to be a trifferent code (of block length n) if for every three distinct codewords x, y, z ϵ C, there is a coordi-nate i ϵ 1, 2, . . . , n where they all differ, that is, x(i), y(i), z(i) = 0, 1, 2. Let T(n) denote the size of the largest trifferent code of block length n. Un-derstanding the asymptotic behavior of T(n) is closely related to determining the zero-error capacity of the (3/2)-channel defined by Elias Eli88, and is a long-standing open problem in the area. Elias had shown that T(n) � 2 � (3/2)n and prior to our work the best upper bound was T(n) � 0.6937 � (3/2)n due to Kurz Kur24. We improve this bound to T(n) � c � n-2/5 � (3/2)n where c is an absolute constant. © 2024 IEEE.

Item Type:	Conference Paper
Publication:	IEEE International Symposium on Information Theory - Proceedings
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords:	Asymptotic analysis; C (programming language), Asymptotic behaviour; Block lengths; Code-words; Upper Bound; Zero-error capacity, Codes (symbols)
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	25 Sep 2024 10:26
Last Modified:	25 Sep 2024 10:26
URI:	http://eprints.iisc.ac.in/id/eprint/86291

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