New Algorithms of Distance-Increasing Mappings from Binary Vectors to Permutations by Swaps
Designs, Codes and Cryptography
On the Construction of Permutation Arrays via Mappings from Binary Vectors to Permutations
Designs, Codes and Cryptography
New simple constructions of distance-increasing mappings from binary vectors to permutations
Information Processing Letters
Discrete Applied Mathematics
A table of upper bounds for binary codes
IEEE Transactions on Information Theory
Distance-preserving mappings from binary vectors to permutations
IEEE Transactions on Information Theory
New distance-preserving maps of odd length
IEEE Transactions on Information Theory
Distance-increasing mappings from binary vectors to permutations
IEEE Transactions on Information Theory
Cyclic constructions of distance-preserving maps
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Distance-increasing maps of all lengths by simple mapping algorithms
IEEE Transactions on Information Theory
A Generalized Upper Bound and a Multilevel Construction for Distance-Preserving Mappings
IEEE Transactions on Information Theory
Distance-Preserving and Distance-Increasing Mappings From Ternary Vectors to Permutations
IEEE Transactions on Information Theory
Simple Distance-Preserving Mappings From Ternary Vectors to Permutations
IEEE Transactions on Information Theory
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A distance-preserving mapping is a one-to-one function $f$ from $p$-ary vectors of length $m$ to $q$-ary vectors of length $n$ such that any two distinct $p$-ary vectors are mapped to two different $q$-ary vectors with an equal or greater Hamming distance. A distance-increasing mapping is a special distance-preserving mapping which strictly increases the distance by at least one if the distance of two distinct input vectors is less than the length of the output vectors. A constant composition code over a $k$-ary alphabet has the property that the numbers of occurrences of the $k$ symbols within a codeword are fixed for each codeword. One of the most important applications of distance-preserving mappings and distance-increasing mappings is to construct constant composition codes, of which the permutation codes are a special subclass. There are two results in this paper. First, we propose a swap-based distance-increasing mapping from binary vectors to quaternary constant composition vectors. Second, we prove that it is impossible to construct any swap-based distance-preserving mappings from binary vectors to ternary constant composition vectors under the swap model that we defined.