Construction Of Constant Composition Codes Research Articles

Partitioned difference families and almost difference sets

Partitioned difference families (PDFs) were first studied by Ding and Yin in conjunction with the construction of constant composition codes (CCCs). In 2008, Yin et al. presented the constructions of a number of infinite classes of PDFs based on known difference sets in GF(q). In this paper, we further investigate the constructions of PDFs by using known almost difference sets in GF(q), and establish some recursive constructions of PDFs. As their applications, we also get a number of perfect difference systems of sets (DSSs) over Zq2 with q odd prime.

A new combinatorial approach to the construction of constant composition codes

Constant composition codes (CCCs) are a new generalization of binary constant weight codes and have attracted recent interest due to their numerous applications. In this paper, a new combinatorial approach to the construction of CCCs is proposed, and used to establish new optimal CCCs.

A Construction for Constant-Composition Codes

By employing the residue polynomials, a construction of constant-composition codes is given. This construction generalizes the one proposed by Xing[16]. It turns out that when d=3 this construction gives a lower bound of constant-composition codes improving the one in [10]. Moreover, for d>3, we give a lower bound on maximal size of constant-composition codes. In particular, our bound for d=5 gives the best possible size of constant-composition codes up to magnitude.

Partitions in finite geometry and related constant composition codes

We look at the construction of constant composition codes (CCCs) from various types of partitions in finite projective spaces. In particular, we construct robust classes of codes using regular spreads of PG(2n−1,q) and Baer subgeometry partitions of PG(2n,q2). For each class of codes, we bound the minimum distance by considering how such partitions can intersect. As such, we prove results about the intersection of regular spreads and Baer subgeometry partitions, two of the classical partitions generated by subgroups of a Singer group. In addition, we examine other partitions of objects embedded in finite projective spaces and their associated codes. In each case, we compare our codes to a code of comparable parameters that meets the Plotkin bound.

On constant composition codes

A constant composition code over a k-ary alphabet has the property that the numbers of occurrences of the k symbols within a codeword is the same for each codeword. These specialize to constant weight codes in the binary case, and permutation codes in the case that each symbol occurs exactly once. Constant composition codes arise in powerline communication and balanced scheduling, and are used in the construction of permutation codes. In this paper, direct and recursive methods are developed for the construction of constant composition codes.