Generalized Sudan's List Decoding for Order Domain Codes

A Syndrome Formulation of the Interpolation Step in the Guruswami-Sudan Algorithm

Let F q be a finite field with q elements and C ⊂ F n q a code of length n. If c ∈ C and h = (h 1 h 2 · · · h n) is a row of a parity check matrix of C, then it is clear that h · c = 0. Such parity checks can therefore be used to test if a given word w ∈ F n q is an element of C, but it turns out that the expressions h · w (usually called syndromes of w) can be useful in decoding algorithms as ...

A Displacement Approach to Decoding Algebraic Codes

Using methods originating in numerical analysis, we will develop a uni ed framework for derivation of eÆcient algorithms for decoding several classes of algebraic codes. We will demonstrate our method by accelerating Sudan's list decoding algorithm for Reed-Solomon codes [22], its generalization to algebraic-geometric codes by Shokrollahi and Wasserman [21], and the improvement of Guruswami and...

Soft-decision decoding of Reed-Muller codes as generalized multiple concatenated codes

In this paper, we present a new soft-decision decoding algorithm for Reed-Muller codes. It is based on the GMC decoding algorithm proposed by Schnabl and Bossert [1] which interprets Reed-Muller codes as generalized multiple concatenated codes. We extend the GMC algorithm to list-decoding (L-GMC). As a result, a SDML decoding algorithm for the first order Reed-Muller codes is obtained. Moreover...

Authentication Schemes based on Physically Unclonable Functions

In this project we investigate di erent hardware authentication schemes based on Physically Unclonable Functions. We start by analyzing the concepts of a fuzzy extractor and a secure sketch from an information-theoretic perspective. We then present a hardware implementation of a fuzzy extractor which uses the code o set construction with BCH codes. Finally, we propose a new cryptographic protoc...

Decoding Hermitian Codes with Sudan's Algorithm