Seminars
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
Forthcoming seminars
Seminar calendar
List of seminars
Archive by years
Register a seminar

Search
RSS
Forthcoming seminars






2022-ary quasigroups and related topics
September 24, 2021 11:00–12:30, Novosibirsk, Sobolev Institute of Mathematics, room 135
 


Embedding in MDS codes and Latin cubes

V. N. Potapov

Number of views:
This page:26

Abstract: An embedding of a code is a mapping that preserves distances between codewords. We prove that any code with code distance $\rho$ and code length $d$ can be embedded into an MDS code with the same code distance and code length but with larger alphabet.

References
  1. T. Evans, “Embedding incomplete Latin squares”, Amer. Math. Monthly, 67:10 (1960), 958–961  crossref  mathscinet  zmath
  2. A. B. Cruse, “On the finite completion of partial Latin cubes”, J. Combinatorial Theory Ser. A, 17:1 (1974), 112–119  crossref  mathscinet  zmath  scopus
  3. C. C. Lindner, “Embedding orthogonal partial Latin squares”, Proc. Amer. Math. Soc., 59:1 (1976), 184–186  crossref  mathscinet  zmath  scopus
  4. D. M. Donovan, E. S. Yazici, “A polynomial embedding of pairs of orthogonal partial Latin squares”, J. Combin. Theory Ser. A, 126 (2014), 24–34  crossref  mathscinet  zmath  scopus
  5. D. M. Donovan, M. Grannell, E. Sule Yazici, “Constructing and embedding mutually orthogonal Latin squares: reviewing both new and existing results”, Comment. Math. Univ. Carolin., 61:4 (2020), 437–457  crossref  mathscinet  zmath
  6. D. S. Krotov, E. V. Sotnikova, “Embedding in $q$-ary $1$-perfect codes and partitions”, Discrete Math., 338:11 (2015), 1856–1859  crossref  mathscinet  zmath  scopus
  7. J. Denes, A. D. Keedwell, Latin squares. New development in the theory and applications, Annals of Discrete Mathematics, 46, North-Holland, 1991  mathscinet  zmath


SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru
 
Contact us:
 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022