Corpus ID: 119618667

On symmetry group of Mollard code

@inproceedings{IYuMogilnykh2014OnSG,
  title={On symmetry group of Mollard code},
  author={I.Yu.Mogilnykh and F.I.Soloveva},
  year={2014}
}
For a pair of given binary perfect codes C and D of lengths t and m respectively, the Mollard construction outputs a perfect code M(C,D) of length tm + t +m, having subcodes C and D, that are obtained from codewords of C and D respectively by adding appropriate number of zeros. In this work we generalize of a result for symmetry groups of Vasil’ev codes [2] and find the group StabD2Sym(M(C,D)). The result is preceded by and partially based on a discussion of ”linearity” of coordinate positions… Expand
2 Citations
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A hierarchical picture of extents of linearity for binary codes is established and a transitivity criterion for perfect binary codes of rank greater by one than the rank of the Hamming code of the same length is derived. Expand
On homogeneous nontransitive binary perfect code
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References

SHOWING 1-10 OF 23 REFERENCES
On the existence of extended perfect binary codes with trivial symmetry group
TLDR
It is proved that for all integers n, and for any integer r, there are perfect codes of length n and rank r with trivial symmetry group Sym(C), i.e. Sym$(C)=${id}. Expand
The Classification of Some Perfect Codes
TLDR
It is shown that if the rank of C is n−m+2 then C is equivalent to a code given by a construction of Phelps, and that any such code is a Vasil'ev code. Expand
On the size of the symmetry group of a perfect code
  • Olof Heden
  • Mathematics, Computer Science
  • Discret. Math.
  • 2011
TLDR
It is shown that for every nonlinear perfect code C of length n and rank r with n-log(n+1), Sym(C) denotes the group of symmetries of C, which considerably improves a bound of Malyugin. Expand
On binary 1-perfect additive codes: Some structural properties
TLDR
A characterization of propelinear codes as codes having a regular subgroup of the full group of isometrics of the code is established and a characterization of the automorphism group of a 1-perfect additive code is given. Expand
Structural properties of binary propelinear codes
TLDR
It is shown that there exists a binary code, the Best code of length 10, size 40 and minimum distance 4, which is transitive but not propelinear, and a lower bound is given on the number of nonequivalent Propelinear perfect binary codes. Expand
A note on the symmetry group of full rank perfect binary codes
  • Olof Heden
  • Computer Science, Mathematics
  • Discret. Math.
  • 2012
Abstract It is proved that the size of the symmetry group Sym ( C ) of every full rank perfect 1-error correcting binary code C of length n is less than or equal to 2 | Sym ( H n ) | / ( n + 1 ) ,Expand
On the Structure of Symmetry Groups of Vasil’ev Codes
TLDR
It is proved that the symmetry group of an arbitrary perfect binary non-full-rank Vasil’ev code of length n is always nontrivial; for codes of rank n − log(n + 1) +1, an attainable upper bound on the order of the symmetry groups is obtained. Expand
On the Construction of Transitive Codes
  • F. Solov'eva
  • Mathematics, Computer Science
  • Probl. Inf. Transm.
  • 2005
TLDR
Application of some known methods of code construction to transitive codes satisfying certain auxiliary conditions yields infinite classes of large-length transitivecodes, in particular, at least at least ⌊k/2⌋2 nonequivalent perfect transitives codes of length n = 2k − 1, k > 4. Expand
Reconstruction theorems for centered functions and perfect codes
The article addresses the centered functions and perfect codes in the space of all binary n-tuples. We prove that all values of a centered function in a ball of radius k ≤ (n + 1)/2 are uniquelyExpand
Theory of Error-correcting Codes
The field of channel coding started with Claude Shannon's 1948 landmark paper. Fifty years of efforts and invention have finally produced coding schemes that closely approach Shannon's channelExpand
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