… a family of paritycheck matrices having column weight 3, and that … of Kirkman triple systems
are presented in the Appendix. … In addition to Steiner and Kirkman triple systems we examine…

… on Kirkman triple systems for a family of parity-check matrices … Kirkman triple systems (KTS)
to derive regular LDPC codes. Kirkman triple systems are defined as theresolvable Steiner …

… Now we show how to construct Steiner triple systems using … ) of the (26,13)-code with three
orthogonal parities for each code bit. … -CDF we can always construct a parity check matrix of a …

… 1, each codeword bit and parity check constraint are … length constructed based on Kirkman
triple systems is studied. The … of the parity-check matrix designed from Kirkman triple systems. …

… Kirkman settle the existence of Steiner triple systems? We give a complete development of
Kirkman's … STS(v) and call the system a Steiner triple system of order v. Similarly, when λ = 2, …

… A Steiner triple system of order 7 is given in Example I.1.3. … large sets of Kirkman triple systems
of order v when v ≡ 3 (mod … KTSs are used to produce low density parity check codes. §VI.…

… Note that when q = 2 this design is a (2, 3, 15)-Steiner triple system which, as noted above,
… by this argument, we obtain equality in (24) if and only if we have equality in (28), which in …

… size 15 corresponds to a solution to Kirkman’s school girl problem originally posed by Kirkman
in 1850 in [10]: “Fifteen young ladies in a school walk out three abreast for seven days in …

Research on the existence of large sets of Kirkman triple systems (LKTS) extends from the
mid-eighteen hundreds to the present. In this paper we review known direct approaches of …

… A Steiner triple system (X, A) is called a Kirkman svstem if the set A admits a pcrtition A = Al
… exists a Kirkman sys-B tern of order u if and only if u = 3 (mod 6). A Steiner triple system (X, A) …