论文标题
直径家庭的一家完美的恒定重量代码来自Steiner系统
A family of diameter perfect constant-weight codes from Steiner systems
论文作者
论文摘要
如果$ s $是一个瞬态度量空间，则$ | c | \ cdot | a | \ le | s | $对于任何距离 - $ d $ code $ c $和set $ a $ a $，``antyode''的直径小于$ d $。对于每个Steiner s $（t，k，n）$ s $ s $，我们显示出存在$ q $ - ar的恒定代码$ c $长度〜$ n $，重量〜$ k $（或$ n-k $）和距离$ d = 2k-t = 2k-t+1 $（分别是$ d = n-t+1 $），$ d = n-t+1 $ a $ and $ digantion $ a $ d-1 $ - $ c $的代码字的支持是$ s $的块（分别是$ s $的块的补充）。我们研究了估计存在此代码的最低价值的问题，并发现$ t $的少量值的最低值。 关键字：直径完美的代码，他码，恒定重量代码，代码 - Astistode绑定，Steiner系统。
If $S$ is a transitive metric space, then $|C|\cdot|A| \le |S|$ for any distance-$d$ code $C$ and a set $A$, ``anticode'', of diameter less than $d$. For every Steiner S$(t,k,n)$ system $S$, we show the existence of a $q$-ary constant-weight code $C$ of length~$n$, weight~$k$ (or $n-k$), and distance $d=2k-t+1$ (respectively, $d=n-t+1$) and an anticode $A$ of diameter $d-1$ such that the pair $(C,A)$ attains the code--anticode bound and the supports of the codewords of $C$ are the blocks of $S$ (respectively, the complements of the blocks of $S$). We study the problem of estimating the minimum value of $q$ for which such a code exists, and find that minimum for small values of $t$. Keywords: diameter perfect codes, anticodes, constant-weight codes, code--anticode bound, Steiner systems.
