On a new code, \([2^n - 1,n,2^{n - 1}]\) (Q1003689)
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scientific article; zbMATH DE number 5523169
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a new code, \([2^n - 1,n,2^{n - 1}]\) |
scientific article; zbMATH DE number 5523169 |
Statements
On a new code, \([2^n - 1,n,2^{n - 1}]\) (English)
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4 March 2009
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In this paper, a new binary linear \([2^n-1, n, 2^{n-1}]\) code is developed. A systematic generator matrix of the new code is designed. The error capability of this code is \(2^{n-2}-1\). It is shown that the minimum weighted codewords of this code hold \(2-(2^n-1, 2^{n-1}, 2^{n-2})\) design, and do not hold 3-design. Also, some other properties of this code are stated and proved.
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linear code
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t-design
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sectioned code
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non-uniform error correction
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