Abstmct-Multilevel constructions of the binary Golay code and the Leech lattice are described. Both constructions are based upon the prvjection of the Golay code and the Leech lattice onto the (6,3,4) hexacode over GF(4). However, unlike the previously reported constructiods, the new multilevel constructions make the three levels independent by way of using a didlerent set of coset representati...

We report on a computer search for complex Golay sequences of short length. All such sequences of length 11 and 13 will be classified.

For every n = 2 k ≥ 16 there exist exactly ⌊(k + 1)/2⌋ mutually nonequiv-alent Z 4-linear extended perfect codes with distance 4. All these codes have different ranks. Codes represented in such a manner are called Z 4-linear. In [5] it is shown that the extended Golay code and the extended Hamming (n, 2 n−log 2 n−1 , 4)-codes (of length n and cardinality 2 n−log 2 n−1 , with distance 4) for eve...

Forney conjectured the existence of a “normal realization” (NR) for the [24,12,8] Golay code in which the code appears as a tetrahedron, with 6 output channel bits at each of the 4 vertices and 2 state bits carried by each of the 6 edges. Although the conjecture was dashed by Vardy, we here give a quasi-cyclic NR exhibiting tetrahedral symmetry, confirming the common wisdom that Forney is never...

This paper presents the history of error control coding, beginning with the early work of Hamming and Golay and continuing through the advent of modern turbo codes.