Block-avoiding sequencings of points in Steiner triple systems

Given an STS(v), we ask if there is a permutation of the points of the design such that no l consecutive points in this permutation contain a block of the design. Such a permutation is called an l-good sequenc-ing. We prove that 3-good sequencings exist for any STS(v) with v\u3e3 and 4-good sequencings exist for any STS(v) with v\u3e71. Similar re-sults also hold for partial STS(v). Finally, we determine the existence or nonexistence of 4-good sequencings for all the nonisomorphic STS(v) with v =7, 9, 13 and 15

Block-avoiding sequencings of points in Steiner triple systems

Given an STS(v), we ask if there is a permutation of the points of the design such that no L consecutive points in this permutation contain a block of the design. Such a permutation is called an L-good sequencing. We prove that 3-good sequencings exist for any STS(v) with v\u3e3and 4-good sequencings exist for any STS(v) with v\u3e71. Similar results also hold for partial STS(v). Finally, we determine the existence or nonexistence of 4-good sequencings for all the nonisomorphic STS(v) with v=7,9,13 and 15

On min-base palindromic representations of powers of 2

A positive integer $N$ is \emph{palindromic in the base $b$} when $N = \sum_{i=0}^{k} c_i b^i$, $c_k\neq 0$,and $c_i=c_{k-i},\; i=0,1,2,...,k$, Focusing on powers of 2, we investigate the smallest base $b$ when $N=2^n$ is palindromic in the base $b$.Comment: 11 page

On orthogonal generalized equitable rectangles

In this note, we give a complete solution of the existence of orthogonal generalized equitable rectangles, which was raised as an open problem in [4]. Key words: orthogonal latin squares, orthogonal equitable rectangles,

Constructions and bounds for codes with restricted overlaps

Non-overlapping codes have been studied for almost 60 years. In such a code, no proper, non-empty prefix of any codeword is a suffix of any codeword. In this paper, we study codes in which over-laps of certain specified sizes are forbidden. We prove some general bounds and we give several constructions in the case of binary codes. Our techniques also allow us to provide an alternative, elementary proof of a lower bound on non-overlapping codes due to Levenshtein [9] in 1964

Constructions and bounds for codes with restricted overlaps

Non-overlapping codes have been studied for almost 60 years. In such a code, no proper, non-empty prefix of any codeword is a suffix of any codeword. In this paper, we study codes in which overlaps of certain specified sizes are forbidden. We prove some general bounds and we give several constructions in the case of binary codes. Our techniques also allow us to provide an alternative, elementary proof of a lower bound on non-overlapping codes due to Levenshtein in 1964.Comment: 25 pages. Extra citations, typos corrected and explanations expande

Orthogonal Arrays of Strength Three from Regular 3-Wise Balanced Designs

The construction given in Kreher, J Combin Des 4 (1996) 67 is extended to obtain new infinite families of orthogonal arrays of strength 3. Regular 3-wise balanced designs play a central role in this construction