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- W2726016837 abstract "We present a result on extendability of specific constant dimension subspace codes. An $(n, M, d, k)$-subspace code over $mathbb{F}_q$ is a set of $M$ $k$-dimensional subspaces of $mathbb{F}_q^n$ having minimum distance $d$.We focus on large $(n, M, 2k-2, k)$-subspace codes over $mathbb{F}_q$. A well-known upper bound on the maximum size of such a code is M leq {n brack 2}_q / {k brack 2}_q. (1) Our main result is the following: Let $n equiv 0 pmod{k}$, $(n-1) equiv 0 pmod{k-1}$ and $1 le delta leq (q+1)/2$.Let $mathcal{C}$ be an $(n, M, 2k-2, k)$-code, with $M = {n brack 2}_q / {k brack 2}_q - delta$. Then $mathcal{C}$ can be extended to an $(n, {n brack 2}_q / {k brack 2}_q , 2k-2, k)$-code ${mathcal C}'$. This result implies that if no $(n, {n brack 2}_q / {k brack 2}_q, 2k-2, k)$-code exists, then the upper bound (1) can be improved by $(q+1)/2$. We give an insight into the technique, coming from finite geometry, that we used to prove this result. We briefly discuss a more general extendability result on some other classes of constant dimension subspace codes whose parameters satisfy specific divisibility conditions. We finally give an application of the mentioned result." @default.
- W2726016837 created "2017-07-14" @default.
- W2726016837 creator A5059848175 @default.
- W2726016837 date "2017-05-30" @default.
- W2726016837 modified "2023-09-26" @default.
- W2726016837 title "On the extendability of particular classes of constant dimension codes" @default.
- W2726016837 hasPublicationYear "2017" @default.
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