A Class of Composite Codes with Minimum Distance 8

We consider linear composite codes based on the $|a+x|b+x|a+b+x|$ construction. For $m\ge 3$ and $r\le 4m+3$, we propose a class of linear composite $[3\cdot 2^m,3\cdot 2^m-r,8]$ codes, which includes the $[24,12,8]$ extended Golay code. We describe an algebraic decoding algorithm, which is valid for any odd $m$, and a simplified version of this algorithm, which can be applied for decoding the Golay code. We give an estimate for the combinational-circuit decoding complexity of the Golay code. We show that, along with correction of triple independent errors, composite codes with minimum distance 8 can also correct single cyclic error bursts and two-dimensional error bytes.