The Editor-in-Chief has retracted this article at the request of the author. After the publication of this article, the author found an error in the proof of Theorem 2.1. The starting point of the proof is the construction of a non-simple t-design from a simple t-design. The proof is incomplete, because it is carried out by only a subset of blocks, and the claim is only valid if the simple design is also a trivial design. As a result, the argument presented does not support the statement in Theorem 2.1, on which the subsequent results are based. As this was one of the key findings of this article, the author considers that the conclusions of this work are unsupported.

Abstract The paper deals with t-designs that can be partitioned into s-designs, each missing a point of the underlying set, called point-missing s-resolvable t-designs, with emphasis on their applications in constructing t-designs. The problem considered may be viewed as a generalization of overlarge sets which are defined as a partition of all the $$\left( {\begin{array}{c}v +1\\ k\end{array}}\right) $$ v + 1 k k-sets chosen from a $$(v+1)$$ ( v + 1 ) -set X into $$(v+1)$$ ( v + 1 ) mutually disjoint s- $$(v,k,\delta )$$ ( v , k , δ ) designs, each missing a different point of X. Among others, it is shown that the existence of a point-missing $$(t-1)$$ ( t - 1 ) -resolvable t- $$(v,k,\lambda )$$ ( v , k , λ ) design leads to the existence of a t- $$(v,k+1,\lambda ')$$ ( v , k + 1 , λ ′ ) design. As a result, we derive various infinite series of 4-designs with constant index using overlarge sets of disjoint Steiner quadruple systems. These have parameters 4- $$(3^n,5,5)$$ ( 3 n , 5 , 5 ) , 4- $$(3^n+2,5,5)$$ ( 3 n + 2 , 5 , 5 ) and 4- $$(2^n+1,5,5)$$ ( 2 n + 1 , 5 , 5 ) , for $$n \ge 2$$ n ≥ 2 , and were unknown until now. We also include a recursive construction of point-missing s-resolvable t-designs and its application.

Abstract The paper introduces a method for constructing 2-resolvable t-designs for $$t=3,4$$ t = 3 , 4 . The main idea is based on the assumption that there exists a partition of a t-design into Steiner 2-designs. A remarkable property of the method is that it enables the construction of 2-resolvable t-designs with a large variety of block sizes. For $$t=4$$ t = 4 , it is required that the Steiner 2-designs of the partition are projective planes and this case would also lead to a construction of 3-resolvable 5-designs. For instance, we show the existence of an infinite series of 3-resolvable 5-designs having $$N=5$$ N = 5 resolution classes with parameters 5- $$(14+8m,7, 10(9+8m)(1+m))$$ ( 14 + 8 m , 7 , 10 ( 9 + 8 m ) ( 1 + m ) ) for any $$m \ge 0$$ m ≥ 0 as a byproduct. Moreover, it turns out that the method is very effective, as it yields infinitely many 2-resolvable 3-designs. However, the question of simplicity of the constructed designs has not been yet investigated.

For communication schemes employing Frequency Hopping/Multiple Frequency Shift Keying modulation, we present an algorithm for finding good non-binary synchronization sequences, which are permutations, to be used with permutation codes to synchronize/resynchronize data in channels with background noise and interference(frequency jamming/fading). For the synchronization sequences, new analytical expressions for the probability of false acquisition are also given. Using simulation results, we show that our synchronization sequences perform better than some conventional non-binary synchronization sequences, in the presence of background noise and interference.