Two-weight ternary codes and the equation y2 = 4 × 3a + 13

A. Bremner; R. Calderbank; P. Hanlon; P. Morton; J. Wolfskill

doi:10.1016/0022-314X(83)90042-2

Two-weight ternary codes and the equation y² = 4 × 3^a + 13

A. Bremner, R. Calderbank, P. Hanlon, P. Morton, J. Wolfskill

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

10 Scopus citations

Abstract

This paper determines the parameters of all two-weight ternary codes C with the property that the minimum weight in the dual code C^⊥ is at least 4. This yields a characterization of uniformly packed ternary [n, k, 4] codes. The proof rests on finding all integer solutions of the equation y² = 4 × 3^a + 13.

Original language	English (US)
Pages (from-to)	212-234
Number of pages	23
Journal	Journal of Number Theory
Volume	16
Issue number	2
DOIs	https://doi.org/10.1016/0022-314X(83)90042-2
State	Published - Apr 1983
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/0022-314X(83)90042-2

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title = "Two-weight ternary codes and the equation y2 = 4 × 3a + 13",

abstract = "This paper determines the parameters of all two-weight ternary codes C with the property that the minimum weight in the dual code C⊥ is at least 4. This yields a characterization of uniformly packed ternary [n, k, 4] codes. The proof rests on finding all integer solutions of the equation y2 = 4 × 3a + 13.",

author = "A. Bremner and R. Calderbank and P. Hanlon and P. Morton and J. Wolfskill",

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AU - Morton, P.

AU - Wolfskill, J.

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AB - This paper determines the parameters of all two-weight ternary codes C with the property that the minimum weight in the dual code C⊥ is at least 4. This yields a characterization of uniformly packed ternary [n, k, 4] codes. The proof rests on finding all integer solutions of the equation y2 = 4 × 3a + 13.

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