论文标题
Gopala-Hemachandra代码重新审视
Gopala-Hemachandra codes revisited
论文作者
论文摘要
Gopala-Hemachandra代码是斐波那契通用代码的变体，并在加密和数据压缩中具有应用。我们表明，$ gh_ {a}（n）$代码始终存在$ a = -2，-3 $和$ -4 $的任何整数$ n \ geq 1 $，因此是通用代码。我们开发了两种新算法来确定是否存在针对给定参数$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $的GH代码。在2010年，巴苏（Basu）和普拉萨德（Prasad）在实验上表明，在$ 1 \ leq n \ leq 100 $和$ 1 \ leq k \ leq 16 $中，最多有$ k $连续的整数，其中$ gh _ { - （4+k）}（4+k）}（n）$不存在。我们将他们的数值结果变成数学定理，并表明它在它们考虑的有限范围之外是有效的。
Gopala-Hemachandra codes are a variation of the Fibonacci universal code and have applications in cryptography and data compression. We show that $GH_{a}(n)$ codes always exist for $a=-2,-3$ and $-4$ for any integer $n \geq 1$ and hence are universal codes. We develop two new algorithms to determine whether a GH code exists for a given set of parameters $a$ and $n$. In 2010, Basu and Prasad showed experimentally that in the range $1 \leq n \leq 100$ and $1 \leq k \leq 16$, there are at most $k$ consecutive integers for which $GH_{-(4+k)}(n)$ does not exist. We turn their numerical result into a mathematical theorem and show that it is valid well beyond the limited range considered by them.
