A class of optimal constant composition codes from GDRPs

Abstract

As a common generalization of constant weight binary codes and permutation codes, constant composition codes (CCCs) have attracted recent interest due to their numerous applications. In this paper, a class of new CCCs are constructed using design-theoretic techniques. The obtained codes are optimal in the sense of their sizes. This result is established, for the most part, by means of a result on generalized doubly resolvable packings which is of combinatorial interest in its own right.

Near generalized balanced tournament designs with block sizes 4 and 5

“…We apply Theorem 2.6 with the starter S = S · (g, 1) and the corresponding adder A = A · (g, 1), where g ∈ C Table 2. {(4,0), (7,6), (2,11),(1,7)} (2, 0) {(2,2), (5,4), (3,6), (10,9)} (2, 0) Proof. We use Table 3 to show the conclusion.…”

“…For (h, u) ∈ { (10,9), (15, 7)}, we take the point set as Z u × Z h . Then we apply Theorem 2.6 with the starter-adder pair (S ∪ (−S ), A ∪ (−A )), where −S = S · (−1, 1).…”

“…{ (8,1), (9,4), (3,3), (4,2),(1,0)} (9,0) { (6,2), (9,2), (7,1), (4,0), (8,0)} (10,0) { (7,2), (9,0), (8,2), (10,4), ( { (11,0), (8,1), (7,3), (2,3), (5,4)} (10,0) { (11,3), (5,2), (7,1), (3,0),(1,1)} (7,0) (4,2), (10,4), (1,3), (3,3)} (5,0) { (6,4), …”

“…{ (11,2), (7,2), (10,0), (4,1), ( (1,5), (6,7), (10,9), (15,9) (4,3), (3,5), (8,6),(15,7)} (3,0) { (5,3), (4,4), (10,6), (3,8), (1,8) 14), (2,14), (3,4), (4,9), { (1,13), (2,13), (3,2), (6,10), (8,4)} (2,0) (15,13) S1 : { (1,5), (2,10), (3,11), (4,9), …”

“…We give a brief description below. For more detailed information on starters and adders, the reader is refered to [6,7,10] and the references therein.…”