Abstract
Subspace code is very useful in the error correction for random network coding. In this paper, subspace code based on flats in affine space over finite fields is constructed. Sphere-packing bound, Wang–Xing–Safavi-Naini bound, anticode bound, Ahlswede–Aydinian bound and Gilbert–Varshamov bound for the size of code based on flats in affine space over finite fields are provided. Finally, we introduce another method of obtaining the anticode bound for the size of code based on flats in affine space from Erdős–Ko–Rado theorem.
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