25 research outputs found
The Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties
A complete classification of the perfect binary one-error-correcting codes of
length 15 as well as their extensions of length 16 was recently carried out in
[P. R. J. \"Osterg{\aa}rd and O. Pottonen, "The perfect binary
one-error-correcting codes of length 15: Part I--Classification," IEEE Trans.
Inform. Theory vol. 55, pp. 4657--4660, 2009]. In the current accompanying
work, the classified codes are studied in great detail, and their main
properties are tabulated. The results include the fact that 33 of the 80
Steiner triple systems of order 15 occur in such codes. Further understanding
is gained on full-rank codes via switching, as it turns out that all but two
full-rank codes can be obtained through a series of such transformations from
the Hamming code. Other topics studied include (non)systematic codes, embedded
one-error-correcting codes, and defining sets of codes. A classification of
certain mixed perfect codes is also obtained.Comment: v2: fixed two errors (extension of nonsystematic codes, table of
coordinates fixed by symmetries of codes), added and extended many other
result
Partial spreads and vector space partitions
Constant-dimension codes with the maximum possible minimum distance have been
studied under the name of partial spreads in Finite Geometry for several
decades. Not surprisingly, for this subclass typically the sharpest bounds on
the maximal code size are known. The seminal works of Beutelspacher and Drake
\& Freeman on partial spreads date back to 1975, and 1979, respectively. From
then until recently, there was almost no progress besides some computer-based
constructions and classifications. It turns out that vector space partitions
provide the appropriate theoretical framework and can be used to improve the
long-standing bounds in quite a few cases. Here, we provide a historic account
on partial spreads and an interpretation of the classical results from a modern
perspective. To this end, we introduce all required methods from the theory of
vector space partitions and Finite Geometry in a tutorial style. We guide the
reader to the current frontiers of research in that field, including a detailed
description of the recent improvements.Comment: 30 pages, 1 tabl
Counting siblings in universal theories
We show that if a countable structure in a finite relational language is
not cellular, then there is an age-preserving such that
many structures are bi-embeddable with . The proof proceeds
by a case division based on mutual algebraicity.Comment: 26 pages; v2 has local corrections in Section 7.
Predicting companies stock price direction by using sentiment analysis of news articles
This paper summarizes our experience teaching
several courses at Metropolitan College of Boston University Computer Science department over five years. A number of innovative teaching techniques are presented in this paper. We
specifically address the role of a project archive, when designing a course. This research paper explores survey results from every running of courses, from 2014 to 2019. During each class, students participated in two distinct surveys: first, dealing with key learning outcomes, and, second, with teaching techniques used. This paper makes several practical recommendations based on the analysis of collected data. The research validates the value of a sound repository of technical term projects and the role such repository plays in effective teaching and learning of computer science courses.Published versio