Decoding Random Binary Linear Codes in 2n/20: How
نویسندگان
چکیده
Decoding random linear codes is a well studied problem with many applications in complexity theory and cryptography. The security of almost all coding and LPN/LWE-based schemes relies on the assumption that it is hard to decode random linear codes. Recently, there has been progress in improving the running time of the best decoding algorithms for binary random codes. The ball collision technique of Bernstein, Lange and Peters lowered the complexity of Stern’s information set decoding algorithm to 2 . Using representations this bound was improved to 2 by May, Meurer and Thomae. We show how to further increase the number of representations and propose a new information set decoding algorithm with running time 2 .
منابع مشابه
Binary Linear Codes with Optimal Scaling and Quasi-Linear Complexity
We present the first family of binary codes that attains optimal scaling and quasi-linear complexity, at least for the binary erasure channel (BEC). In other words, for any fixed δ > 0, we provide codes that ensure reliable communication at rates within ε > 0 of the Shannon capacity with block length n = O(1/ε2+δ), construction complexity Θ(n), and encoding/decoding complexity Θ(n log n). Furth...
متن کاملComputing the error linear complexity spectrum of a binary sequence of period 2n
Binary sequences with high linear complexity are of interest in cryptography. The linear complexity should remain high even when a small number of changes are made to the sequence. The error linear complexity spectrum of a sequence reveals how the linear complexity of the sequence varies as an increasing number of the bits of the sequence are changed. We present an algorithm which computes the ...
متن کاملList Decoding for Binary Goppa Codes
This paper presents a list-decoding algorithm for classical irreducible binary Goppa codes. The algorithm corrects, in polynomial time, approximately n− p n(n− 2t− 2) errors in a length-n classical irreducible degree-t binary Goppa code. Compared to the best previous polynomialtime list-decoding algorithms for the same codes, the new algorithm corrects approximately t/2n extra errors.
متن کاملDecoding Algorithms for Random Linear Network Codes
We consider the problem of efficient decoding of a random linear code over a finite field. In particular we are interested in the case where the code is random, relatively sparse, and use the binary finite field as an example. The goal is to decode the data using fewer operations to potentially achieve a high coding throughput, and reduce energy consumption. We use an on-the-fly version of the ...
متن کاملOn Efficient Decoding and Design of Sparse Random Linear Network Codes
Random linear network coding (RLNC) in theory achieves the max-flow capacity of multicast networks, at the cost of high decoding complexity. To improve the performance-complexity tradeoff, we consider the design of sparse network codes. A generation-based strategy is employed in which source packets are grouped into overlapping subsets called generations. RLNC is performed only amongst packets ...
متن کامل