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In its original design an RS code is designed for operation over the Galois eld GF(2m ), and its code length is n = 2m 1 One interesting application of these codes is the design of RS codes over the extended Galois eld GF(28 ) = GF(256), because any element of a code vector in these codes is itself a vector of 8 bits, or a byte An RS code designed over this eld, able to correct any error pattern of size t = 2 or less, is the RS code CRS (255, 251) A table of the codewords in this code would be enormous However, the rst page of the table (or set of codewords at the top of the table) would contain codewords with 0 s only in the most signi cant message positions.

, & Cadman, E C (1993) Needle exchange decreases the prevalence of HIV-1 proviral DNA in returned syringes in New Haven, Connecticut American Journal of Medicine, 95, 14 20 Herek, G M (1999) AIDS and stigma American Behavioral Scientist, 42, 1106 116 1 Ho, D D, Neumann, A U, Perelson, A S, Chen, W, Leonard, J M, & Markowitz, M (1995) Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection Nature, 373, 123 126 Holtgrave, D R (Ed) (1998) Handbook of economic evaluation of HIV prevention programs New York: Plenum Press Holtgrave, D R, & Pinkerton, S D (1997) Updates of cost of illness and quality of life estimates for use in economic evaluations of HIV prevention programs Journal of Acquired Immune De ciency Syndromes, 16, 54 62 Jemmott, J B, Jemmott, L S, & Fong, G T (1992).

Therefore a shortened RS code can be formed by taking this page of codewords and deleting the positions that are 0 s in all the codewords on this page More speci cally, a shortened RS code can be constructed by setting sRS message symbols to zero, where 1 sRS < k Then the length of the code is n sRS symbols, the number of message symbols is k sRS and the number of parity symbols is n k as before, where all the symbols remain in GF(2m ) The generator polynomial and the error-correcting capability of the shortened code is the same as that of the unshortened code, but the code is no longer cyclic since not all cyclic shifts of codewords in the shortened code are also in the shortened code For this reason the shortened code is said to be quasi-cyclic.

Reductions in HIV risk-associated sexual behaviors among Black male adolescents: Effects of an AIDS prevention intervention American Journal of Public Health, 82, 372 377 Jemmott, J B, Jemmott, L S, & Fong, G T (1998) Abstinence and safer sex HIV risk-reduction interventions for African American adolescents: A randomized controlled trial Journal of the American Medical Association, 279, 1529 1536..

In this way, an RS code can be designed without the restriction of having a xed code length n = 2m 1, so that the code length can be signi cantly reduced, without losing any good property of the main code Thus, shortened RS codes CRS (28, 24) and CRS (32, 28) are obtained from the original RS code CRS (255, 251) by setting sRS = 227 and sRS = 223, respectively, and both the shortened codes have the same error-correction capability as that of the main code CRS (255, 251), which is t = 2 The main code and the shortened versions of this code all have a minimum distance dmin = 5 These two codes are the constituent codes of the CD error-control coding system..

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RESULTS This section presents the results of the call setup automation experiments using Type A IP-PSTN GWs. The experimental setup is shown in Figure B-1. We used only one pair one making outgoing calls and the other receiving incom-

1 Proof: Let u(x) = |X | be the uniform probability mass function over X, and let p(x) be the probability mass function for X. Then