Construction of 2n prime-sequence codes for optical code division multiple access

The construction of a special family of 2ⁿ codes, so-called `2ⁿ prime-sequence´ codes, for optical code division multiple access (CDMA) has recently been investigated. Since the codes pose the algebraic properties of the prime-sequence and 2ⁿ codes, those optical coding architectures, which are especially designed for either of the two codes, can be jointly employed to optimally cope with various constraints (e.g. power budget and cost) imposed by the systems using optical CDMA. As a result, an optical coding architecture, which is particularly attractive for ultrafast optical signal processing and waveguide implementation for the future, high capacity all-optical CDMA networks with potentially 3 dB ideal power ideal, has been proposed. However, the cardinality of the codes is very limited and shown to approach zero when the code weight is sufficiently large. A generalised family of 2ⁿ prime-sequence codes, which has the same cardinality as the original prime-sequence codes, is constructed and supported with complete mathematical proofs