The standard genetic code multiplet structure as well as the correct degeneracies, class by class, are all extracted from the (unique) number 23!, the order of the permutation group of 23 objects.

It is established that for any q > 2 the permutation automorphism group of a q-ary Hamming code of length n = (q − 1)/(q− 1) is isomorphic to the unitriangular group UTm(q).

A permutation with no fixed points is called a derangement.The subset $mathcal{D}$ of a permutation group is derangement if all elements of $mathcal{D}$ are derangement.Let $G$ be a permutation group, a derangementgraph is one with vertex set $G$ and derangement set $mathcal{D}$ as connecting set. In this paper, we determine the spectrum of derangement graphs of order a product of three primes.

A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudorandom nature, and the new codes are quasi-cyclic. Graph isomorphisms and automorphisms are identified and used in an efficient search for good codes. Graphs with girth as large as 12 wer...

In [1], the author provided a Gray code for the set of n-length permutations with a given number of left-to-right minima in inversion array representation. In this paper, we give the first Gray code for the set of n-length permutations with a given number of left-to-right minima in one-line representation. In this code, each permutation is transformed into its successor by a product with a tran...

We discuss experimental results of a versatile nonbinary modulation and channel code appropriatefor two-dimentional page-oriented holographic memories. An enumerative permutation code is used to provide a modulation code that permits a simple maximum-likelihood detection scheme. Experimental results from the IBM Demon testbed are used to characterize the performance and feasibility of the propo...

Equidistant Frequency Permutation Arrays are combinatorial objects of interest in coding theory. A frequency permutation array is a type of constant composition code in which each symbol occurs the same number of times in each codeword. The problem is to find a set of codewords such that any pair of codewords are a given uniform Hamming distance apart. The equidistant case is of special interes...

A new scheme providing security against passive attackers in linear network coding is proposed. Throughput efficiency, low algorithm complexity, and high adaptability/applicability are the major design factors that are considered in this security protocol. A bijective permutation map defined over the code field is utilized to generate the randomness that is required for masking the plain inform...

This work concerns formal descriptions of DNA code properties and related (un)decidability questions. This line of research allows us to give a property as input to an algorithm, in addition to any regular language, which can then answer questions about the language and the property. Here we define DNA code properties via transducers and show that this method is strictly more expressive than th...