The complexity of maximum likelihood decoding of the ReedSolomon codes [q−1, k]q is a well known open problem. The only known result [4] in this direction states that it is at least as hard as the discrete logarithm in some cases where the information rate unfortunately goes to zero. In this paper, we remove the rate restriction and prove that the same complexity result holds for any positive i...

We propose an improvement to Sudan's algorithm for decoding Reed-Solomon codes beyond half of their minimum distance, and its generalisation to algebraic-geometric codes. Both algorithms, in their original version, involve factorisation of polynomials. The main idea consists in replacing factorisation by an iterative root nding procedure of low complexity based on Newton approximation. In the c...

FRoM the FIeld | 155 The purpose of this article is not to provide a critical analysis of the Regional Assistance Mission to the Solomon Islands (RAMSI) or a robust platform for lessons learned. Rather, it offers a general introduction to the country and an overview of a stabilization and reconstruction operation with a different framework than many of the operations that the United States has ...

Baldi et al. proposed a variant of McEliece’s cryptosystem. The main idea is to replace its permutation matrix by adding to it a rank 1 matrix. The motivation for this change is twofold: it would allow the use of codes that were shown to be insecure in the original McEliece’s cryptosystem, and it would reduce the key size while keeping the same security against generic decoding attacks. The aut...

Title of dissertation: PERFORMANCE ANALYSIS OF ALGEBRAIC SOFT-DECISION DECODING OF REED-SOLOMON CODES Andrew Duggan, Masters of Science, 2006 Thesis directed by: Professor Alexander Barg Department of Electrical and Computer Engineering We investigate the decoding region for Algebraic Soft-Decision Decoding (ASD) of Reed-Solomon codes in a discrete, memoryless, additive-noise channel. An expres...