A new method for constructing minimum-redundancy prefix codes is described. This method does not explicitly build a Huffman tree; instead it uses a property of optimal codes to find the codeword length of each weight. The running time of the algorithm is shown to be O(nk), which is asymptotically faster than Huffman’s algorithm when k = o(log n), where n is the number of weights and k is the nu...

The standard genetic code is known to be much more efficient in minimizing adverse effects of misreading errors and one-point mutations in comparison with a random code having the same structure, i.e. the same number of codons coding for each particular amino acid. We study the inverse problem, how the code structure affects the optimal physico-chemical parameters of amino acids ensuring the hi...

It is proven that for every random variable with a countably infinite set of outcomes and finite entropy there exists an optimal prefix code which can be constructed from Huffman codes for truncated versions of the random variable, and that the average lengths of any sequence of Huffman codes for the truncated versions converge to that of the optimal code. Also, it is shown that every optimal i...

It is proven that for every random variable with a countably infinite set of outcomes and finite entropy there exists an optimal prefix code which can be constructed from Huffman codes for truncated versions of the random variable, and that the average lengths of any sequence of Huffman codes for the truncated versions converge to that of the optimal code. Also, it is shown that every optimal i...

The brackets of ``[n, k, d]'' signal that C is linear, and n is the length, k the dimension, and d the minimum weight of C. The bound was proved by Griesmer in 1960 for q=2 and generalized by Solomon and Stiffler in 1965. Over the years, much effort has gone into constructing codes meeting the bound or showing, for selected parameter values, that they do not exist. This effort is part of the mo...

Single-track Gray codes are cyclic Gray codes with codewords of length n, such that all the n tracks which correspond to the n distinct coordinates of the codewords are cyclic shifts of the first track. We investigate the structure of such binary codes and show that there is no such code with 2n codewords when n is a power of 2. This implies that the known codes with 2n 2n codewords, when n is ...

In this paper, we study vector codes with all-symbol locality, where the local code is either a Minimum Bandwidth Regenerating (MBR) code or a Minimum Storage Regenerating (MSR) code. In the first part, we present vector codes with all-symbol MBR locality, for all parameters, that have both optimal minimum-distance and optimal rate. These codes combine ideas from two popular codes in the distri...

A constant-composition code is a special constant-weight code under the restriction that each symbol should appear a given number of times in each codeword. In this correspondence, we give a lower bound for the maximum size of the -ary constant-composition codes with minimum distance at least 3. This bound is asymptotically optimal and generalizes the Graham–Sloane bound for binary constant-wei...

Novel coding schemes are introduced and relationships between optimal codes and Huffman codes are discussed. It is shown that, for finite source alphabets, the Huffman coding is the optimal coding, and conversely the optimal coding needs not to be the Huffman coding. It is also proven that there always exists the optimal coding for infinite source alphabets. We show that for every random variab...

We previously proposed an Orthogonal Code Hopping Multiplexing(OCHM) scheme as a new statistical multiplexing scheme in synchronous downlink. OCHM enables a large number of users to share a limited number of code channels through statistical multiplexing. In this paper, we obtain the optimal code rate in several traffic load environments by simulation and summarize the appropriate traffic load ...