Linear Codes and Syndrome Decoding - Maple Application Center
Application Center Applications Linear Codes and Syndrome Decoding

Linear Codes and Syndrome Decoding

: José Luis Gómez Pardo
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Implementation of the encoding and decoding algorithms associated to an error-correcting linear code. Such a code can be characterized by a generator matrix or by a parity-check matrix and we introduce, as examples, the [7, 4, 2] binary Hamming code, the [24, 12, 8] and [23, 12, 7] binary Golay codes and the [12, 6, 6] and [11, 6, 5] ternary Golay codes. We give procedures to compute the minimum distance of a linear code and we use them with the Hamming and Golay codes. We show how to build the standard array and the syndrome array of a linear code and we give an implementation of syndrome decoding. Finally, we simulate a noisy channel and use the Hamming and Golay codes to show how syndrome decoding allows error correction on text messages.

Application Details

Publish Date: June 06, 2019
Created In: Maple 2017
Language: English

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