Pless symmetry code[1,2] 

Description

Also called a Pless double circulant code. A member of a family of self-dual ternary \([2p+2,p+1]_3\) codes for any prime \(p \equiv -1\) modulo 6. See [3; Sec. 10.5][4; pg. 87] for explicit constructions.

Parent

Cousin

  • Ternary Golay code — The Pless symmetry code for \(p=5\) is the extended ternary Golay code.

References

[1]
V. Pless, On a new family of symmetry codes and related new five-designs, BAMS 75 (1969), 1339-1342
[2]
V. Pless, “Symmetry codes over GF(3) and new five-designs”, Journal of Combinatorial Theory, Series A 12, 119 (1972) DOI
[3]
W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes (Cambridge University Press, 2003) DOI
[4]
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups (Springer New York, 1999) DOI
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Zoo Code ID: pless_symmetry

Cite as:
“Pless symmetry code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/pless_symmetry
BibTeX:
@incollection{eczoo_pless_symmetry, title={Pless symmetry code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/pless_symmetry} }
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“Pless symmetry code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/pless_symmetry

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/dual/pless_symmetry.yml.