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Optimal Divisible Binary Codes from Gray-Homogeneous Images of Codes over Rk;m

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Abstract (2. Language): 
In this work, we nd a form for the homogeneous weight over the ring Rk;m, using the related theoretical results from the literature. We then use the rst order Reed-Muller codes to nd a distance-preserving map that takes codes over Rk;m to binary codes. By considering cyclic, constacyclic and quasicyclic codes over Rk;m of di erent lengths for di erent values of k and m, we construct a considerable number of optimal binary codes that are divisible with high levels of divisibility. The codes we have obtained are also quasicyclic with high indices and they are all self-orthogonal when km  4. The results, which have been obtained by computer search are tabulated.
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REFERENCES

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