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Universal Bounds for Size and Energy of Codes of Given Minimum and Maximum Distances
- Source :
- IEEE Transactions on Information Theory. 67:3569-3584
- Publication Year :
- 2021
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2021.
-
Abstract
- We employ signed measures that are positive definite up to certain degrees to establish Levenshtein-type upper bounds on the cardinality of codes with given minimum and maximum distances, and universal lower bounds on the potential energy (for absolutely monotone interactions) for codes with given maximum distance and cardinality. The distance distributions of codes that attain the bounds are found in terms of the parameters of Levenshtein-type quadrature formulas. Necessary and sufficient conditions for the optimality of our bounds are derived. Further, we obtain upper bounds on the energy of codes of fixed minimum and maximum distances and cardinality.<br />submitted, 34 pages
- Subjects :
- FOS: Computer and information sciences
Discrete mathematics
Linear programming
Information Theory (cs.IT)
Computer Science - Information Theory
020206 networking & telecommunications
02 engineering and technology
Positive-definite matrix
Library and Information Sciences
Potential energy
Upper and lower bounds
Computer Science Applications
Quadrature (mathematics)
Monotone polygon
FOS: Mathematics
94B65
0202 electrical engineering, electronic engineering, information engineering
Mathematics - Combinatorics
Cardinality (SQL statements)
Combinatorics (math.CO)
Energy (signal processing)
Information Systems
Mathematics
Subjects
Details
- ISSN :
- 15579654 and 00189448
- Volume :
- 67
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Information Theory
- Accession number :
- edsair.doi.dedup.....634fa359647fb9fad4c5fac40d5e8e57