Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical error-correcting codes. Here we examine symmetry properties for codeword stabilized (CWS) quantum codes, which is the most general framework for constructing quantum error-correcting codes known to date. A CWS code Q can be repres...

We develop a general framework to prove Krafttype inequalities for prefix-free permutation codes for source coding with various notions of permutation code and prefix. We also show that the McMillan-type converse theorem in most of these cases does not hold, and give a general form of a counterexample. Our approach is more general and works for other structures besides permutation codes. The cl...

In 2000 Babson and Steingŕımsson introduced the notion of vincular patterns in permutations. They show that essentially all well-known Mahonian permutation statistics can be written as combinations of such patterns. Also, they proved and conjectured that other combinations of vincular patterns are still Mahonian. These conjectures were proved later: by Foata and Zeilberger in 2001, and by Foata...

Let G be the automorphism group of the four-dimensional cube, a group of order24 . 4 ! = 384. The binary codes associated with the 32-dimensional permutationrepresentation of G on the edges of the cube are investigated. There are about 400 suchcodes, one of which is a [32, 17, 8] code, having twice as many codewords as the[32, 16, 8] extended quadratic residue code. __________<l...

The linear code equivalence problem is to decide whether two linear codes over Fq are identical up to a linear isometry of the Hamming space. The support splitting algorithm [23] runs in polynomial time for all but a negligible proportion of all linear codes, and solves the latter problem by recovering the isometry when it is just a permutation of the code support. While for a binary alphabet i...

In this paper, we introduce a new encoding scheme that explicitly targets the minimization of the bus energy due to the crosstalk capacitances between adjacent bus lines. The key transformation operated by the code consists of a permutation of the bus lines, implemented directly during physical design; as a desirable consequence, no additional encoding/decoding logic is required at the bus boun...

The linear code equivalence problem is to decide whether two linear codes over Fq are identical up to a linear isometry of the Hamming space. The support splitting algorithm [25] runs in polynomial time for all but a negligible proportion of all linear codes, and solves the latter problem by recovering the isometry when it is just a permutation of the code support. While for a binary alphabet i...

We discuss the combination of permutation codes and M-ary frequency shift keying. We show that this combination has special properties that can be used in power-line communications: e.g. constant envelopes, and error correction capability for impulsiveand narrow band noise. We give a simple convolutional encoding and decoding scheme. The outputs of a binary convolutional codes are mapped onto c...

The symmetric group Sn on n letters is a metric space with respect to the Hamming distance. The corresponding isometry group is well known to be isomorphic to the wreath product Sn oS2. A subset of Sn is called a permutation code or a permutation array, and the largest possible size of a permutation code with minimum Hamming distance d is denoted by M(n, d). Using exhaustive search by computer ...

Permutation decoding is a technique which involves finding a subset S, called PDset, of the permutation automorphism group PAut(C) of a code C in order to assist in decoding. A method to obtain s-PD-sets of size s + 1 for partial permutation decoding for the binary linear Hadamard codes Hm of length 2 m, for all m ≥ 4 and 1 < s ≤ b(2m −m− 1)/(1 + m)c, is described. Moreover, a recursive constru...