Abstract: Let p be a prime and let b be an integer. MDS b-symbol codes are a direct generalization of MDS codes. The γ-constacyclic codes of length pˢ over the finite commutative chain ring Fₚm [u]/ < u² > had been classified into four distinct types, where is a nonzero element of the field Fₚm. Let C₃ be a code of Type 3. In this paper, we obtain the b-symbol distance db(C₃) of the code C₃. Using this result, necessary and sufficient conditions under which C₃ is an MDS b-symbol code are given.
Abstract: This paper studies a special class of linear codes, called skew cyclic codes, over the ring R= Fq+uFq+…+uk-1Fq, where q is a prime power. A Gray map ɸ from R to Fq and a Gray map ɸ' from Rn to Fnq are defined, as well as an automorphism Θ over R. It is proved that the images of skew cyclic codes over R under map ɸ' and Θ are cyclic codes over Fq, and they still keep the dual relation.
Abstract: We considered repeated-root cyclic codes whose
block length is divisible by the characteristic of the underlying field.
Cyclic self dual codes are also the repeated root cyclic codes. It is
known about the one-level squaring construction for binary repeated
root cyclic codes. In this correspondence, we introduced of two
level squaring construction for binary repeated root cyclic codes of
length 2a b , a > 0, b is odd.
Abstract: Scale Time Offset Robust Modulation (STORM) [1]–
[3] is a high bandwidth waveform design that adds time-scale
to embedded reference modulations using only time-delay [4]. In
an environment where each user has a specific delay and scale,
identification of the user with the highest signal power and that
user-s phase is facilitated by the STORM processor. Both of these
parameters are required in an efficient multiuser detection algorithm.
In this paper, the STORM modulation approach is evaluated with
a direct sequence spread quadrature phase shift keying (DS-QPSK)
system. A misconception of the STORM time scale modulation is that
a fine temporal resolution is required at the receiver. STORM will
be applied to a QPSK code division multiaccess (CDMA) system
by modifying the spreading codes. Specifically, the in-phase code
will use a typical spreading code, and the quadrature code will
use a time-delayed and time-scaled version of the in-phase code.
Subsequently, the same temporal resolution in the receiver is required
before and after the application of STORM. In this paper, the bit error
performance of STORM in a synchronous CDMA system is evaluated
and compared to theory, and the bit error performance of STORM
incorporated in a single user WCDMA downlink is presented to
demonstrate the applicability of STORM in a modern communication
system.