Constructions of the Golay Codes: A Survey

Constructing the Extended Binary Golay Code

Coding theory is the subject which is concerned with how information can be sent over a noisy channel. A code then is a collection of codewords which are strings of a fixed number of letters from an alphabet. Some of these strings are codewords others are not. When a codeword is sent over a channel there is a probability less than /2 that each letter in the codeword will be changed, thus introd...

Golay complementary array pairs

Constructions and nonexistence conditions for multi-dimensional Golay complementary array pairs are reviewed. A construction for a d-dimensional Golay array pair from a (d+1)-dimensional Golay array pair is given. This is used to explain and expand previously known constructive and nonexistence results in the binary case.

Z4-Linear Perfect Codes

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...

Generalized Reed-Muller codes and power control in OFDM modulation

Controlling the peak-to-mean envelope power ratio (PMEPR) of Orthogonal Frequency Division Multiplexed (OFDM) transmissions is a notoriously di cult problem, though one which is of vital importance for the practical application of OFDM in low-cost applications. The utility of Golay complementary sequences in solving this problem has been recognised for some time. In this paper, a powerful theor...

Constru tions of the Golay Codes: A Survey