We propose upper and lower bounds on the minimum code length of linear codes with specified minimum Hamming distance and dual distance. From these

Primal-dual distance bounds of linear codes with application to cryptography

Primal-dual distance bounds of linear codes with application to cryptography

application to cryptography

In this paper we study a first-order primal-dual algorithm for convex optimization problems with known saddle-point structure. We prove convergence to a saddle-point with rate O(1/N) in finite dimensions, which is optimal for the complete class of non-smooth problems we are considering

Two kinds of contemporary developments in cryptography are examined. Widening applications of teleprocessing have given rise to a need for new types of cryptographic systems, which minimize the need for secure key distribution channels and supply the equivalent of a written signature. This paper

ABSTRACT. A method is given for the construction of linear codes with prescribed min-imum distance and also prescribed minimum distance of the dual code. This works for codes over arbitrary finite fields. In the case of binary codes Matsumoto et al. showed how such codes can be used to construct

Our main result is a reduction from worst-case lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear

Abstract not found

: the soft channel and a priori inputs, and the extrinsic value. The extrinsic value is used as an a priori value for the next iteration. Decoding algorithms in the log-likelihood domain are given not only for convolutional codes hut also for any linear binary systematic block code. The iteration