On Bonisoli’s theorem and the block codes of Steiner triple systems
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Assmus Jr. E.F., Mattson Jr. H.F.: Error-correcting codes: an axiomatic approach. Inform. Control 6, 315–330 (1963).
Beth T., Jungnickel D., Lenz H.: Design Theory, 2nd edn. Cambridge University Press, Cambridge (1999).
Bonisoli A.: Every equidistant linear code is a sequence of dual Hamming codes. Ars Comb. 18, 181–186 (1983).
Borges J., Rifà J., Zinoviev V.A.: On $$q$$ q -ary linear completely regular codes with $$\rho = 2$$ ρ = 2 and antipodal dual. Adv. Math. Commun. 4, 567–578 (2010).
Calderbank R., Kantor W.M.: The geometry of two-weight codes. Bull. Lond. Math. Soc. 18, 97–122 (1986).
Coupland J.: On the construction of certain Steiner systems. Ph. D. thesis, University College of Wales (1975).
De Clerck F., Durante N.: Constructions and characterizations of classical sets in $$PG(n,q)$$ P G ( n , q ) . In: Current Research Topics in Galois Geometry, pp. 1–33. Nova Science Publishers, New York (2012).
Delsarte P.: An algebraic approach to the association schemes of coding theory. Ph. D. thesis, Philips Research Laboratories (1973).
Doyen J., Hubaut X., Vandensavel M.: Ranks of incidence matrices of Steiner triple systems. Math. Z. 163, 251–259 (1978).
Hall Jr. M.: Combinatorial Theory, 2nd edn. Wiley, New York (1986).
Hamada N.: On the $$p$$ p -rank of the incidence matrix of a balanced or partially balanced incomplete block design and its applications to error correcting codes. Hiroshima Math. J. 3, 153–226 (1973).
Huffman W.C., Pless V.: Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge (2003).
Jungnickel D., van Lint J.H. (Eds.): Designs and Codes—A memorial tribute to Ed Assmus. Des. Codes Cryptogr. 17 and 18 (1999).
MacWilliams F.J., Sloane N.J.A.: The Theory of Error-Correcting Codes. North-Holland, New York (1977).
Teirlinck L.: Combinatorial structures. Ph. D. Thesis, University of Brussels, Brussels (1976).
Tonchev V.D.: Linear perfect codes and a characterization of the classical designs. Des. Codes Cryptogr. 17, 121–128 (1999).
Tonchev V.D.: A mass formula for Steiner triple systems STS $$(2^{n}-1)$$ ( 2 n - 1 ) of 2-rank $$2^n -n$$ 2 n - n . J. Comb. Theory Ser. A 95, 197–208 (2001).
Tonchev V.D., Weishaar R.S.: Steiner triple systems of order 15 and their codes. J. Stat. Plan. Inference 58, 207–216 (1997).