论文标题
一些互补的灰色代码
Some complementary Gray codes
论文作者
论文摘要
二进制n-tuples的互补灰色代码是，当所有元组互补时，它与自身相同。这相当于代码上半年的补充与下半年相同。我们将互补的概念推广到Q-ary n-tupers，n-stet和排列的固定尺寸组合，在每种情况下，都构造了互补的灰色代码。我们尽可能地放松身心，与违反必要条件的情况互补的概念，并在弱的定义中构造灰色代码：当n很奇怪时，这些二进制n-tupers n ofd ofd off ofd and ock ofd ofd ofd and n ofd and os od ofd and n of ofd os q-ary n-tupless n ne奇数且q是偶数。最后，用于置换的构造中的引理提供了第一个已知的循环灰色代码，用于特定的多种群体系列的排列。
A complementary Gray code for binary n-tuples is one that, when all the tuples are complemented, is identical to itself; this is equivalent to the complement of the first half of the code being identical to the second half. We generalize the notion of complementary to q-ary n-tuples, fixed size combinations of an n-set and permutations and, in each case, construct complementary Gray codes. We relax, as weakly as possible, the notions of complementary to cases where necessary conditions for existence are violated and construct Gray codes within the weakened definitions: these include binary n-tuples when n is odd and Lee metric q-ary n-tuples when n is odd and q is even. Finally a lemma used in the construction for permutations offers the first known cyclic Gray code for the permutations of a particular family of multisets.
