The Structure of Dual Schubert Union Codes

In this paper, we prove that Schubert union codes are Tanner codes constructed from the point-line incidence geometry inherited from the Grassmannian. Our proof is based on an iterative encoding algorithm for Tanner codes. This encoder determines the entries of a code word of a Tanner code from the...

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Bibliographic Details
Published in:IEEE transactions on information theory 2017-03, Vol.63 (3), p.1425-1433
Main Author: Pinero, Fernando L.
Format: Article
Language:English
Subjects:
Algorithms
Bipartite graph
Codes
error correction codes
Geometry
Hamming weight
Information theory
Linear codes
Parity check codes
Set theory
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Summary:In this paper, we prove that Schubert union codes are Tanner codes constructed from the point-line incidence geometry inherited from the Grassmannian. Our proof is based on an iterative encoding algorithm for Tanner codes. This encoder determines the entries of a code word of a Tanner code from the entries in a given subset of its positions. As a result, we find sufficient conditions on the initial positions such that a code word is determined from the component codes only. This algorithm has linear complexity in the code length. We also use this encoder to determine the minimum distance of Schubert union codes in terms of the minimum distance of the Schubert varieties contained therein.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2017.2650207