@inproceedings{852b33ca2ba04acab595aab80eb6a94d,

title = "Reconstructing Sets of Latin Squares, Linear and Equivalent to Linear Codes",

abstract = "We consider the reconstruction problem concerning latin squares, sets of mutually orthogonal latin squares as well as linear and equivalent to linear codes in a vector space over a finite field. With regard to this problem we discuss related topics on intersection of combinatorial objects of the same class. An algorithm reconstructing latin squares and its sets is presented. By this way it is shown for q 3, 4, 5, 7 that the Bose complete set of mutually orthogonal latin squares of order q with 2q-1 or less blank entries in each square at the same places is reconstructed uniquely. We also point some recently obtained results on the maximum intersection of linear and equivalent to linear codes, and their applications as well.",

keywords = "complete set of MOLS, equivalent codes, finite field, intersection, isometry, isotopy, latin square, linear code, MDS code, MOLS, pseudolinear code, reconstructing algorithm",

author = "Gorkunov, {Evgeny V.} and Danilko, {Vitaly R.}",

note = "Funding Information: This research is supported by the Russian Foundation for Basic Research (Project 19–01–00682) and the Programme for Fundamental Scientific Research of SB RAS No. I.5.1 (Project 0314–2019–0016).; 16th International Symposium {"}Problems of Redundancy in Information and Control Systems{"}, REDUNDANCY 2019 ; Conference date: 21-10-2019 Through 25-10-2019",

year = "2019",

month = oct,

doi = "10.1109/REDUNDANCY48165.2019.9003314",

language = "English",

series = "2019 16th International Symposium {"}Problems of Redundancy in Information and Control Systems{"}, REDUNDANCY 2019",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "47--51",

booktitle = "2019 16th International Symposium {"}Problems of Redundancy in Information and Control Systems{"}, REDUNDANCY 2019",

address = "United States",

}