On self-dual affine-invariant codes

AbstractAn extended cyclic code of length 2m over GF(2) cannot be self-dual for even m. For odd m, the Reed-Muller code [2m, 2m−1, 2(m+1)2] is affine-invariant and self-dual, and it is the only such code for m = 3 or 5. We describe the set of binary self-dual affine-invariant codes of length 2m for m = 7 and m = 9. For each odd m, m ⩾ 9, we exhibit a self-dual affine-invariant code of length 2m over GF(2) which is not the self-dual Reed-Muller code. In the first part of the paper, we present the class of self-dual affine-invariant codes of length 2m over GF(2r), and the tools we apply later to the binary codes

ON THE MINIMUM WEIGHT CODEWORDS OF SOME BINARY BCH CODES

International audienceWe give the true minimum distances of some BCH codes of length 255 and 511, which were not known. We describe the set of the minimum weight codewords of the BCH codes with designed distance 2^{m-2}-

The application of forward error correction techniques in wireless ATM

Bibliography: pages 116-121.The possibility of providing wireless access to an ATM network promises nomadic users a communication tool of unparalleled power and flexibility. Unfortunately, the physical realization of a wireless A TM system is fraught with technical difficulties, not the least of which is the problem of supporting a traditional ATM protocol over a non-benign wireless link. The objective of this thesis, titled "The Application of Forward Error Correction Techniques in Wireless ATM' is to examine the feasibility of using forward error correction techniques to improve the perceived channel characteristics to the extent that the channel becomes transparent to the higher layers and allows the use of an unmodified A TM protocol over the channel. In the course of the investigation that this dissertation describes, three possible error control strategies were suggested for implementation in a generic wireless channel. These schemes used a combination of forward error correction coding schemes, automatic repeat request schemes and interleavers to combat the impact of bit errors on the performance of the link. The following error control strategies were considered : 1. A stand alone fixed rate Reed-Solomon encoder/decoder with automatic repeat request. 2. A concatenated Reed-Solomon, convolution encoder/decoder with automatic request and convolution interleaving for the convolution codec. 3. A dynamic rate encoder/decoder using either a concatenated Reed-Solomon, convolution scheme or a Reed-Solomon only scheme with variable length Reed-Solomon words

A Microprocessor based hybrid system for digital error correction

The design of a microprocessor based hybrid system for digital error correction is presented. It is shown that such a system allows for implementation of several cyclic codes at a variety of throughput rates providing variable degrees of error correction depending on current user requirements. The theoretical basis for encoding and decoding of binary BCH codes is reviewed. Design and implementation of system hardware and software are described. A method for injection of independent bit errors with controllable statistics into the system is developed, and its accuracy verified by computer simulation. This method of controllable error injection is used to test performance of the designed system. In analysis, these results demonstrate the flexibility of operation provided by the hybrid nature of the system. Finally, potential applications and modifications are presented to reinforce the wide applicability of the system described in this thesis

Computer-assisted proofs in geometry and physics

Thesis (Ph. D.)--Massachusetts Institute of Technology, Department of Mathematics, 2013.Cataloged from PDF version of thesis.Includes bibliographical references.In this dissertation we apply computer-assisted proof techniques to two problems, one in discrete geometry and one in celestial mechanics. Our main tool is an effective inverse function theorem which shows that, in favorable conditions, the existence of an approximate solution to a system of equations implies the existence of an exact solution nearby. This allows us to leverage approximate computational techniques for finding solutions into rigorous computational techniques for proving the existence of solutions. Our first application is to tight codes in compact spaces, i.e., optimal codes whose optimality follows from linear programming bounds. In particular, we show the existence of many hitherto unknown tight regular simplices in quaternionic projective spaces and in the octonionic projective plane. We also consider regular simplices in real Grassmannians. The second application is to gravitational choreographies, i.e., periodic trajectories of point particles under Newtonian gravity such that all of the particles follow the same curve. Many numerical examples of choreographies, but few existence proofs, were previously known. We present a method for computer-assisted proof of existence and demonstrate its effectiveness by applying it to a wide-ranging set of choreographies.by Gregory T. Minton.Ph.D

Authentication Schemes based on Physically Unclonable Functions

In this project we investigate different 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 offset construction with BCH codes. Finally, we propose a new cryptographic protocol for PUF authentication based upon polynomial interpolation using Sudan\u27s list-decoding algorithm. We provide preliminary results into the feasibility of this protocol, by looking at the practicality of finding a polynomial that can be assigned as a cryptographic key to each device

Authentication Schemes based on Physically Unclonable Functions

In this project we investigate dierent 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 oset construction with BCH codes. Finally, we propose a new cryptographic protocol for PUF authentication based upon polynomial interpolation using Sudan\u27s list-decoding algorithm. We provide preliminary results into the feasibility of this protocol, by looking at the practicality of nding a polynomial that can be assigned as a cryptographic key to each device

Modeling and computational issues in the development of batch processes

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 1997.Includes bibliographical references (p. 385-401).by Russell John Allgor.Ph.D