Let G be the automorphism group of the four-dimensional cube, a group of order $2^4 \cdot 4! = 384$. The binary codes associated with the 32-dimensional permutation representation of G on the edges of the cube are investigated. There are about 400 such codes, one of which is a $[32, 17, 8]$ code, having twice as many codewords as the $[32, 16, 8]$ extended quadratic residue code.

The binary-image-compression problem is analyzed using irreducible cover of maximal rectangles. A bound on the minimum-rectangular-cover problem for image compression is given under certain conditions that previously have not been analyzed. It is demonstrated that for a simply connected image, the irreducible cover proposed uses less than four times the number of the rectangles in a minimum cover. With n pixels in a square, the parallel algorithm for obtaining the irreducible cover uses (n/log n) concurrent-read-exclusive write (CREW) processors in O(log n) time.>

Blokh and Zyablov's concatenating method, constructionsX, Y1of Sloane et al., and AIItop's constructionXXare applied to various codes to obtain new binary linear codes. These codes improve on the recent updated Helgert-Stinaff table of Verhoeff.