Graduate Thesis Or Dissertation
 

New bounds and constructions for error control codes

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/z890rx42b

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  • The bulk of the theory on error control codes has been developed under the fault assumption of random (symmetric) errors, where 1 → 0 and 0 → 1 errors are equally likely. In the past few years, several applications have emerged in which the observed errors are highly asymmetric. This has prompted the study of codes that offer a combination of symmetric and asymmetric error control capabilities. This research is a part of this ongoing study. The main results of the research are listed below. 1. New upper bounds on t-unordered codes. Exact bounds are established in some cases. 2. A new method for constructing constant weight distance four codes that gives the best known bounds in several cases. 3. A new method for constructing single asymmetric error correcting codes. The method establishes several new lower bounds. 4. A construction for symmetric error correcting code. The code is suited for a photon channel and other highly asymmetric channels because it has far fewer 1's than 0's. The code uses one extra bit of redundancy over the BCH code in almost all cases, and it is relatively easy to encode and decode. 5. A new construction for systematic double asymmetric error correcting code. The resulting code is easier to decode than the BCH code and is optimal in several cases. The code has fewer 1's than 0's. 6. A new construction for double symmetric error correcting linear code. The resulting code is easier to decode than the BCH code and is optimal in several cases. 7. A new construction for linear codes. The construction yields best known codes in many cases.
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