Codes From Symmetry Groups, and a $[32, 17, 8]$ Code

Codes from Symmetry Groups, and a [32, 17, 8] Code

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...

On the [32, 16, 8] BCH and quadratic residue codes

Visual Discrimination of the 17 Plane Symmetry Groups

Within most of the 17 plane symmetry groups, individual symmetry operations act in multiple, nonequivalent ways. This, and the fact that many groups can be realized on the basis of different unit cells and generating regions, poses difficulties for visual discrimination and identification. Because of inherent confounds, only few of the groups can be studied by traditional experimental methodolo...

Intrinsic Symmetry Groups of Links with 8 and Fewer Crossings

We present new computations of “intrinsic” symmetry groups for knots and links of 8 or fewer crossings. The standard symmetry group for a link is the mapping class group MCG(S, L) or Sym(L) of the pair (S, L). Elements in this symmetry group can (and often do) fix the link and act nontrivially only on its complement. We ignore such elements and focus on the “intrinsic” symmetry group of a link,...

Linear codes from projectivity groups

In this talk, we consider linear error–correcting codes that are constructed from orbits of a projectivity group of PG(k, Fq). In this way, we obtain linear codes with better parameters with respect to the previously known ones, and improve several entries in MinT’s tables (http://mint.sbg.ac.at/) and Markus Grassl’s Tables (www.codetables.de). Among these new codes, we found of particular inte...