On the Number of 1-Perfect Binary Codes: A Lower Bound
نویسندگان
چکیده
We present a construction of 1-perfect binary codes, which gives a new lower bound on the number of such codes. We conjecture that this lower bound is asymptotically tight.
منابع مشابه
The (non-)existence of perfect codes in Lucas cubes
A Fibonacci string of length $n$ is a binary string $b = b_1b_2ldots b_n$ in which for every $1 leq i < n$, $b_icdot b_{i+1} = 0$. In other words, a Fibonacci string is a binary string without 11 as a substring. Similarly, a Lucas string is a Fibonacci string $b_1b_2ldots b_n$ that $b_1cdot b_n = 0$. For a natural number $ngeq1$, a Fibonacci cube of dimension $n$ is denoted by $Gamma_n$ and i...
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عنوان ژورنال:
- IEEE Trans. Information Theory
دوره 54 شماره
صفحات -
تاریخ انتشار 2008