Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 26 for “"linear codes"”.
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Multitree search decoding of linear codes
ISSN:1616-671X
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Contributions to the decoding of linear codes over Z4
… hard and soft decision decoding techniques for linear codes over Z4, all of which, offer substantial coding gains over classical algebraic decoding. We focus only on codes which are free, i.e., (n, k, d) linear codes whose canonical images over GF(2) are (n, k) linear codes of the same minimum …
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Multiplicative codes of Reed-Muller type
This is a comprehensive study of multiplicative codes of Reed-Muller type and their applications. Our codes apply to the elds of cryptography and coding theory, especially to multiparty computa- tion and secret sharing schemes. We also study the AB method to analyze the minimum distance of linear …
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Algebraic geometric codes over rings
… widely and successfully applied to the study of linear codes over finite fields since the early 1980's. Recently, there has been an increased interest in the study of linear codes over finite rings. In this thesis, we combine these two approaches to coding theory by introducing and studying …
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Developments in Nonlinear Codes and Distance Preserving Maps
Linear codes are generally easier to construct and correct errors than nonlinear codes. However, for some parameters nonlinear binary codes are more efficient than any linear binary code. Some of these codes can be constructed as linear codes in higher powers of two and then converted to binary …
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Optimal Codes and Entropy Extractors
… and a study of the properties of Hadamard codes. We find of particular interest the Griesmer bound, which is a strong result known to be true only for linear codes. We try to extend it to all codes, and we can determine many parameters for which the Griesmer bound is true also for nonlinear …
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The construction of DNA codes using a computer algebra system
… This concerns the construction of new DNA codes which satisfy certain combinatorial constraints, using an alphabet of four symbols. The interest in these codes arises because it is possible to synthesise short single strands of DNA known as oligonucleotides. The codes can be useful in the …
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Minimum distance of error correcting codes versus encoding complexity, symmetry, and pseudorandomness
… the minimum distance of binary error correcting codes from the following perspectives: * The problem of deriving bounds on the minimum distance of a code given constraints on the computational complexity of its encoder. * The minimum distance of linear codes that are symmetric in the sense of …
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Coded Distributed Function Computation
… Two serendipitous consequences of the (bi-)linear nature of matrix multiplication is that it is both highly parallelizable and that linear codes can be applied to it; making the coding theory approach a fruitful avenue of research for this particular optimization of distributed computing.</p>
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Secure network coding with a cost criterion
… the messages of interest. We make use of random linear codes in anticipation for decentralized implementation of the scheme, and focus on the problem of finding the multicast subgraph. As an exact algorithmic solution is difficult, we propose two heuristic solutions, and compare their …
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Making Coding Practical: From Servers to Smartphones
… Among them is random network coding with random linear codes, in which a node in a network topology transmits a linear combination of incoming, or source, packets to its outgoing links. Theoretically, the high computational complexity of random linear codes (RLC) is well known, and is used to …
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CODE SMOOTHING, UNIFORM DISTRIBUTIONS, AND APPLICATIONS
… divergence. Our results show that random linear codes, as well as structured families like Reed-Muller and LDPC codes, are highly effective at smoothing. Building on these code families, we develop practical and effective coding schemes for use in wiretap channel settings. We also study …
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Anchor Free Mobility
… a seamless handover solution using random linear codes. In the proposed solution, coded traffic is disseminated in either a broadcast or a multicast fashion from source to the destination(s), where destination(s) selection is based on mobility prediction, in a proactive manner during …
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Error correcting binary codes
… 1, 2, 3, and 5, we are primarily concerned with linear codes in which the encoder is a linear transformation of then dimensional vector space containing the message vectors into the vector space of dimension n + k, such that certain errors can be located or at least detected. In Chapter 1, we …
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Graceful codes : fundamental limits and constructions
… from noisy observations Error correcting codes are means of adding redundancy to the data to enable better recovery Most commonly, codes are designed to recover data in a regime where the statistics of the noise are kept constant In a number of applications, however, it is required that …
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Error-correction on non-standard communication channels
… In this thesis, low-density parity-check codes and codes related to them are applied to non-standard channels. First, we look at time-varying noise modelled by a Markov channel. A low-density parity-check code decoder is modified to give an improvement of over 1dB. Secondly, novel codes …
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Non-orthogonal multiple access using guessing random additive noise decoding aided macrosymbols
… we introduce multiple access channel (MAC) codes, which are codes that are used to split the channel rate between users and correct errors due to the MAI. Each user has their information bits encoded with independent MAC codes, which can be short, low rate linear codes such as cyclic …
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On the construction, dimensionality, and decoding of linear block code trellises
… improved through the use of longer error control codes and soft-decision maximum-likelihood (ML) decoding. Unfortunately, the implementation of such techniques is limited by the computational requirements of the decoder. In this thesis, we consider several aspects of trellis-based ML, and …
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Symmetries in algebraic Property Testing
… local testing, symmetry and dual structure in linear codes, by showing both positive and negative results. On the negative side, we exhibit a counterexample to a conjecture proposed by Alon, Kaufman, Krivelevich, Litsyn, and Ron aimed at providing general sufficient conditions for testing. We …
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