IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Regular Section
Can the BMS Algorithm Decode Up to $\lfloor \frac{d_G-g-1}{2}\ floor$ Errors? Yes, but with Some Additional Remarks
Shojiro SAKATAMasaya FUJISAWA
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2010 Volume E93.A Issue 4 Pages 857-862

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Abstract

It is a well-known fact [7], [9] that the BMS algorithm with majority voting can decode up to half the Feng-Rao designed distance dFR. Since dFR is not smaller than the Goppa designed distance dG, that algorithm can correct up to $\lfloor \frac{d_G-1}{2}\ floor$ errors. On the other hand, it has been considered to be evident that the original BMS algorithm (without voting) [1], [2] can correct up to $\lfloor \frac{d_G-g-1}{2}\ floor$ errors similarly to the basic algorithm by Skorobogatov-Vladut. But, is it true? In this short paper, we show that it is true, although we need a few remarks and some additional procedures for determining the Groebner basis of the error locator ideal exactly. In fact, as the basic algorithm gives a set of polynomials whose zero set contains the error locators as a subset, it cannot always give the exact error locators, unless the syndrome equation is solved to find the error values in addition.

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© 2010 The Institute of Electronics, Information and Communication Engineers
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