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The Standard Array: A Useful Tool for Understanding and Analyzing Linear Block Codes

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Using the standard array, you can quickly estimate the error-correcting capability of a linear block code of any dimension. It might seem that the visual benefits are only present for small codes, but this is not so. By using the concepts of the standard array, you can achieve insight into the workings of large as well as small codes. This article walks you through some numerical examples and provides insight for understanding the algebra behind error-correcting block codes.
This article is excerpted from Digital Communications: Fundamentals and Applications, Second Edition (Prentice-Hall, 2001, ISBN 0-13-084788-7).
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The standard array can be thought of as an organizational tool, a filing cabinet that contains all of the possible 2n binary n-tuples (called vectors)—nothing missing, and nothing replicated. The entire space of n-tuples is called the vector space, Vn. At first glance, the benefits of this tool seem limited to small block codes, because for code lengths beyond n = 20 there are millions of n-tuples in Vn. However, even for large codes, the standard array allows visualization of important performance issues, such as bounds on error-correction capability, as well as possible tradeoffs between error correction and detection.

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Editor's Note: This article is offered in PDF in order to provide consistency and clarity to the in-text equations.
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