# Self-dual codes over the Kleinian four group

@article{Hhn2000SelfdualCO, title={Self-dual codes over the Kleinian four group}, author={Gerald H{\"o}hn}, journal={Mathematische Annalen}, year={2000}, volume={327}, pages={227-255} }

Abstract.We introduce self-dual codes over the Kleinian four group K=Z2×Z2 for a natural quadratic form on Kn and develop the theory. Topics studied are: weight enumerators, mass formulas, classification up to length 8, neighbourhood graphs, extremal codes, shadows, generalized t-designs, lexicographic codes, the Hexacode and its odd and shorter cousin, automorphism groups, marked codes. Kleinian codes form a new and natural fourth step in a series of analogies between binary codes, lattices…

## 50 Citations

Graph-based classification of self-dual additive codes over finite fields

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It is proved that the minimum distance of a self-dual additive code is related to the minimum vertex degree in the associated graph orbit, and it is shown that some of these codes have highly regular graph representations.

On the classification of all self-dual additive codes over GF(4) of length up to 12

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A survey of self-dual codes, written for the Handbook of Coding Theory. Self-dual codes are important because many of the best codes known are of this type and they have a rich mathematical theory.…

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All extremal (optimal) codes of lengths 13 and 14 are classified, and many extremal codes oflength 15 and 16 are constructed, and some new extremalcodes of lengths 17,18,19, and 21 are constructed.

s-Extremal Additive Codes over GF(4)

- Computer Science2006 IEEE International Symposium on Information Theory
- 2006

This paper introduces a concept of s-extremality for additive self-dual codes over F4, gives a bound on the length of these codes with even distance d, and classify them up to minimum distance d = 4.

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New self-dual codes over GF(4) with the highest known minimum weights

- Computer Science, MathematicsIEEE Trans. Inf. Theory
- 2001

The purpose of this correspondence is to construct new Hermitian self-dual codes over GF(4) of lengths 22, 24, 26, 32, and 34 which have the highest known minimum weights. In particular, for length…

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- 2007

All extremal (optimal) codes of lengths 13 and 14 are classified, and many extremal codes oflength 15 and 16 are constructed, and some new extremalcodes of lengths 17,18,19, and 21 are constructed.

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Quantum stabilizer codes, lattices, and CFTs

- Computer ScienceArXiv
- 2020

It is shown that quantum error-correcting codes, those of the stabilizer type, are related to Lorentzian lattices and non-chiral CFTs, and thus Narain C FTs are defined.

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