Constructions of skew-tolerant and skew-detecting codes

[l] T.A. Gulliver and V.K. Bhargava, “Some best rate l / p and rate (p l ) / p systematic quasi-cyclic codes,” IEEE Trans. Inform. Theory, vol. IT-37, pp. 552-555, May 1991. [2] T.A. Gulliver and V.K. Bhargava, “Nine good rate (m l) /pm quasicyclic codes,” IEEE Trans. Inform. Theory, vol. IT-38, pp. 1366-1369, July 1992. [3] G.E. S6guin and G. Drolet, “The theory of 1-generator quasi-cyclic codes,” Dep. of Elec. Comput. Eng., Royal Military College of Canada, Kingston, Ont., Canada, June 1990. [4] F.J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. New York North-Holland, 1977. [5] P.P. Greenough and R. Hill, “Optimal temary quasi-cyclic codes,” Designs, Codes and Cryptography, vol. 2, pp. 81-91, 1992. [6] T. Verhoeff, “An updated table of minimum-distance bounds for binary linear codes,” IEEE Trans. Inform. Theory, vol. IT-33, pp. 665-680, Sept. 1987, revised Jan. 1989. AbstractRecently the paradigm of skew-tolerant parallel asynchronous communication was introduced, along with constructions for codes that can tolerate or detect skew. Some of these constructions were improved in [SI. In this paper these constructions are improved upon hrther, and we prove that the new constructions are, in a certain sense, optimal.