Increasing the Minimum Distance of Codes by Twisting

@article{Akbari2015IncreasingTM,
  title={Increasing the Minimum Distance of Codes by Twisting},
  author={Marzieh Akbari and Neil I. Gillespie and Cheryl E. Praeger},
  journal={Electron. J. Comb.},
  year={2015},
  volume={25},
  pages={3}
}
Twisted permutation codes, introduced recently by the second and third authors, belong to the family of frequency permutation arrays. Like some other codes in this family, such as the repetition permutation codes, they are obtained by a repetition construction applied to a smaller code (but with a "twist" allowed). The minimum distance of a twisted permutation code is known to be at least the minimum distance of a corresponding repetition permutation code, but in some instances can be larger… 
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References

SHOWING 1-10 OF 21 REFERENCES

CHARACTERISATION OF A FAMILY OF NEIGHBOUR TRANSITIVE CODES

A family of neighbour transitive codes, in particular, the alphabet almost simple neighbour transitives codes with minimum distance at least 3, and for which the group X has a non-trivial intersection with the base group of Aut().If C is such a code, it is shown that, up to equivalence, there exists a subcode � that can be completely described, and it is proved that any finite group can be identified in a natural way with a neighbours transitive code.

Twisted permutation codes

It is shown that a lower bound for the minimum Distance of a twisted permutation code is the minimum distance of a repetition permutations code.

Decoding Frequency Permutation Arrays Under Chebyshev Distance

This paper first proves lower and upper bounds on the size of FPA, then gives several constructions of FPAs, and some of them come with efficient encoding and decoding capabilities and are shown to be locally decodable.

Frequency permutation arrays

This article establishes basic properties of FPAs, and provides direct constructions for FPAs using a range of combinatorial objects, including polynomials over finite fields, combinatorially designs, and codes.

Neighbour transitivity on codes in Hamming graphs

This paper examines codes with the property that some group of automorphisms acts transitively on the set of neighbours of the code, and obtains sufficient conditions for a neighbour transitive group to fix the code setwise.

On constant composition codes

Correcting Limited-Magnitude Errors in the Rank-Modulation Scheme

This work defines codes protecting against spike errors, called limited-magnitude rank-modulation codes (LMRM codes), and presents several constructions for these codes, some resulting in optimal codes.

Equidistant frequency permutation arrays and related constant composition codes

This paper studies the special class of equidistant constant composition codes of type CCC(n, d, μm) (where n = mμ), which correspond toequidistant frequency permutation arrays and establishes various properties of these objects and gives constructions for optimal families of codes.

Error-correcting codes for rank modulation

It is shown that the adjacency graph of permutations is a subgraph of a multi-dimensional array of a special size, a property that enables code designs based on Lee- metric codes.

The geometry of the classical groups

classical groups Download eBook pdf epub tuebl mobi. A short bibliography on classical groups QMUL Maths. Geometry of G P V. handbook of computational group theory Download eBook. Classical Groups…