Displaying similar documents to “On mixed codes with covering radius 1 and minimum distance 2.”

Codes that attain minimum distance in every possible direction

Gyula Katona, Attila Sali, Klaus-Dieter Schewe (2008)

Open Mathematics

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The following problem motivated by investigation of databases is studied. Let 𝒞 be a q-ary code of length n with the properties that 𝒞 has minimum distance at least n − k + 1, and for any set of k − 1 coordinates there exist two codewords that agree exactly there. Let f(q, k)be the maximum n for which such a code exists. f(q, k)is bounded by linear functions of k and q, and the exact values for special k and qare determined.

Ternary constant weight codes.

Östergård, Patric R.J., Svanström, Mattias (2002)

The Electronic Journal of Combinatorics [electronic only]

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Creation of unequal error protection codes for two groups of symbols

Eugeniusz Kuriata (2008)

International Journal of Applied Mathematics and Computer Science

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This article presents problems of unequal information importance. The paper discusses constructive methods of code generation, and a constructive method of generating asymptotic UEP codes is built. An analog model of Hamming's upper bound and Hilbert's lower bound for asymptotic UEP codes is determined.

Defect theorem in the plane

Włodzimierz Moczurad (2007)

RAIRO - Theoretical Informatics and Applications

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We consider the defect theorem in the context of labelled polyominoes, , two-dimensional figures. The classical version of this property states that if a set of words is not a code then the words can be expressed as a product of at most words, the smaller set being a code. We survey several two-dimensional extensions exhibiting the boundaries where the theorem fails. In particular, we establish the defect property in the case of three dominoes ( × 1 or 1 × rectangles).