Classification of Graeco‐Latin Cubes | Zendy

Kokkala Janne I. | Zendy; Östergård Patric R. J. | Zendy

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Classification of Graeco‐Latin Cubes

Author(s) -

Kokkala Janne I.,

Östergård Patric R. J.

Publication year - 2015

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.21400

Subject(s) - mathematics , combinatorics , equivalence (formal languages) , minimum distance , code (set theory) , separable space , order (exchange) , discrete mathematics , latin square , computer science , mathematical analysis , set (abstract data type) , finance , economics , programming language , rumen , chemistry , food science , fermentation

A q ‐ary code of length n , size M , and minimum distance d is called an( n , M , d ) q code. An( n , q k , d ) q code with d = n − k + 1 is said to be maximum distance separable (MDS). Here one‐error‐correcting ( d = 3 ) MDS codes are classified for small alphabets. In particular, it is shown that there are unique (5, 5 3 , 3) 5 and (5, 7 3 , 3) 7 codes and 12 , 484 equivalence classes of (5, 8 3 , 3) 8 codes. The( 5 , q 3 , 3 ) q codes are equivalent to certain pairs of mutually orthogonal Latin cubes of order q , called Graeco‐Latin cubes.

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