Lemma for Linear Feedback Shift Registers and DFTs Applied to Affine Variety CodesReport as inadecuate



 Lemma for Linear Feedback Shift Registers and DFTs Applied to Affine Variety Codes


Lemma for Linear Feedback Shift Registers and DFTs Applied to Affine Variety Codes - Download this document for free, or read online. Document in PDF available to download.

Download or read this book online for free in PDF: Lemma for Linear Feedback Shift Registers and DFTs Applied to Affine Variety Codes
In this paper, we establish a lemma in algebraic coding theory that frequently appears in the encoding and decoding of, e.g., Reed-Solomon codes, algebraic geometry codes, and affine variety codes. Our lemma corresponds to the non-systematic encoding of affine variety codes, and can be stated by giving a canonical linear map as the composition of an extension through linear feedback shift registers from a Grobner basis and a generalized inverse discrete Fourier transform. We clarify that our lemma yields the error-value estimation in the fast erasure-and-error decoding of a class of dual affine variety codes. Moreover, we show that systematic encoding corresponds to a special case of erasure-only decoding. The lemma enables us to reduce the computational complexity of error-evaluation from On^3 using Gaussian elimination to Oqn^2 with some mild conditions on n and q, where n is the code length and q is the finite-field size.



Author: Hajime Matsui

Source: https://archive.org/







Related documents