Abstract/Details

Sign codes from number fields


1999 1999

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Abstract (summary)

Three new families of binary linear codes are created from a number field. They are created by looking at the “signs” of the embedding of the units into the real numbers, the 2-adic numbers and then a combination of the two embeddings. The transmission rates of these codes are described in terms of the class group of the number field. Then lower bounds are found for the transmission rates of the codes. In the case of the real sign code, heuristic results of Cohen and Lenstra are used to determine the probability of certain rates occurring. A property of the minimum distance is discussed and a relationship between the minimum distances of the three codes is proven.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences, Linear codes, Number fields, Sign codes
Title
Sign codes from number fields
Author
Murray, Maura Ann
Number of pages
46
Publication year
1999
Degree date
1999
School code
0118
Source
DAI-B 60/11, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780599530454, 0599530456
Advisor
Hayes, David R.
University/institution
University of Massachusetts Amherst
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9950190
ProQuest document ID
304513565
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304513565
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