Binary Golay Spreading Sequences and Reed-Muller Codes for Uplink Grant-Free NOMA

Complete Mutually Orthogonal Golay Complementary Sets From Reed-Muller Codes

Recently Golay complementary sets were shown to exist in the subsets of second-order cosets of a q-ary generalization of the first-order Reed–Muller (RM) code. We show that mutually orthogonal Golay complementary sets can also be directly constructed from second-order cosets of a q-ary generalization of the first-order RM code. This identification can be used to construct zero correlation zone ...

Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes

We present a range of coding schemes for OFDM transmission using binary, quaternary, octary, and higher order modulation that give high code rates for moderate numbers of carriers. These schemes have tightly bounded peak-to-mean envelope power ratio (PMEPR) and simultaneously have good error correction capability. The key theoretical result is a previously unrecognized connection between Golay ...

Quantum Reed-Muller Codes

This paper presents a set of quantum Reed-Muller codes which are typically 100 times more effective than existing quantum Reed-Muller codes. The code parameters are [[n, k, d]] = [[2, ∑r l=0 C(m, l) − ∑m−r−1 l=0 C(m, l), 2 m−r ]] where 2r + 1 > m > r.

Generalized Reed-Muller Codes

the possible choices for n and k are rather thinly distributed in the class of all pairs (n, k) with k ~ n--and it is, therefore, often inefficient to make use of such codes in concrete situations (that is, when a desired pair (n, k) is far from any achievable pair). We have succeeded in overcoming this difficulty by generalizing the Reed-Muller codes in such a way that they exist for every pai...

Peak-to-mean power control and error correction for OFDM transmission using Golay sequences and Reed-Muller codes