Restricted Hamming-Huffman Trees

We study a special case of Hamming-Huffman trees, in which both data compression and error detection are tackled on the same structure. Given hypercube Q n dimension , we interested some aspects its vertex neighborhoods. For subset L vertices neighborhood is defined as union neighborhoods . The minimum problem that determining cardinality over all those sets This well-known has already been solved. Our interest lies optimal remains open related to In this work, consider restricted version called [ k ]-HHTs, admit symbol leaves at most different levels. present an algorithm build [2]-HHTs. uniform frequencies, prove HHT always [5]-HHT there exists [4]-HHT. Also, considering experimental results, conjecture tree [3]-HHT.