Abstract: A method of lattice-quantizing an eight-long data point to minimize storage requirements by acquiring the data point, multiplying each coordinate of the data point by {square root over (2)} to form an inflated data point, rounding each coordinate of the rounded and inflated data point to the nearest integer, modulo-two reducing each coordinate of the rounded and inflated data point to form an initial codeword, multiplying a parity-check matrix of an eight-bit Extended Hamming Code by the result of the last step to form a syndrome, correcting any single-bit errors and double-bit errors, if any, in the initial codeword and the rounded and inflated data point, transforming the coordinate system of the initial codeword to an extended quadratic residue form, creating a signal packet, and transmitting the signal packet to a receiver.

Abstract: A method of lattice quantizing a 24-long data point to minimize storage requirements by acquiring the data point, multiplying each coordinate of the data point by the square root of 8 to form an inflated data point, finding the closest point of the inflated Leech lattice by any method, creating a signal packet, and transmitting the packet to a receiver.