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One interesting property of cyclic block codes is that the number of parity check bits the code adds to the message vector is equal to the degree of the generator polynomial. Thus, and independently of the size of the data packet to be transmitted, the CRC for the standard Ethernet, for instance, always adds 32 bits of redundancy. In the case of the standard protocol Ethernet, the data packet size varies from k = 512 to k = 12,144 bits. The k information bits are the rst part of the whole message, and are considered as a polynomial m(X ), which is followed by the n k = 32 redundancy bits that result from the division of the shifted message polynomial X n k m(X ) by g(X ). The receiver does the same operation on the message bits, so that if the redundancy calculated at the receiver is equal to the redundancy sent in the FCS, then the packet is accepted as a valid one. A retransmission of the packet is required if the recalculated redundancy is different from the contents of the FCS. Consider a simple example of this procedure, using the cyclic block code Ccyc (7, 4) introduced in Example 3.3. Assume that the message m = (1010) has to be transmitted. After encoding this message, the resulting code vector is c = (0011010), where the redundancy is in bold. One way of performing the decoding of this code vector is to recalculate at the receiver the redundancy obtained by encoding the message vector m = (1010), and by verifying that

:s: >'n (A + B) -

Kirshenbaum, J (1983, July 25) Coping, fitfully, with the sports world s growing case load Sports Illustrated, 59, 9 10 Kunz, J L (1997) Drink and be active The associations between drinking and participation in sports Addiction Research, 5, 439 450 Larimer, M E, & Cronce, J M (2002) Identification, prevention and treatment: A review of individual-focused strategies to reduce problematic alcohol consumption by college students Journal of Studies on Alcohol, 63(Suppl 14), 148 163 Larimer, M E, Kilmer, J R, & Lee, C M (2005) College student drug prevention: A review of individually-oriented prevention strategies Journal of Drug Issues, 35, 431 455 Leadbetter, W B (1995) Anti-inflammatory therapy in sports injury: The role of corticosteroid injections Clinics in Sports Medicine, 14, 353 412 Leichliter, J S, Meilman, P W, Presley, C A, & Cashin, J R (1998).

Alcohol use and related consequences among students with varying levels of involvement with college athletics Journal of American College Health, 46, 257 262 Leonard, W L (1998) The influence of physical activity and theoretically relevant variables in the use of drugs: The deterrence hypothesis revisited Journal of Sport Behavior, 21, 421 434 Lorente, F O, Souville, M, Griffet, J, & Gr lot, L (2004) Participation in sports and alcohol consumption among French adolescents Addictive Behaviors, 29, 941 946 MacCallum, J (1986, June 30) The cruelest thing ever Sports Illustrated, 64, 20 24 Madden, P A, & Grube, J W (1994) The frequency and nature of alcohol and tobacco advertising in televised sports, 1990 through 1992 American Journal of Public Health, 84, 297 299 Mandell, A J (1979) The Sunday syndrome: A unique pattern of amphetamine abuse indigenous to American professional football Clinical Toxicology, 15, 225 232.

Marcello, R J, Danish, S J, & Stolberg, A (1989) An evaluation of strategies developed to prevent substance abuse among student-athletes Sport Psychologist, 3, 196 211 Marlatt, G A, & Donovan, D M (Eds) (2005) Relapse prevention New York: Guilford Press Marlatt, G A, & Witkiewitz, K (2005) Relapse prevention for alcohol and drug problems In G A Marlatt & D M Donovan (Eds), Relapse prevention (pp 1 44) New York: Guilford Press Marshall, E (1979) Drugging of football players curbed by central monitoring plan, NFL claims Science, 203, 626 628 Martens, M P, Cox, R H, Beck, N C, & Heppner, P P (2003) Measuring motivations for intercollegiate athlete alcohol use:.

is as follows: IF F1 is SM AND F2 is MD THEN D U4 11:24

(1.29)

(16.27)

Fedewa, MM, Oegema, TR, Jr, Schwartz, MH, MacLeod, A, Lewis, JL (1998) Chondrocytes in culture produce a mechanically functional tissue J Orthop Res 16: 227 236 Fink, C, Ergun, S, Kralisch, D, Remmers, U, Weil, J, Eschenhagen, T (2000) Chronic stretch of engineered heart tissue induces hypertrophy and functional improvement FASEB J 14: 669 679 Frank, EH, and Grodzinsky, AJ (1987) Cartilage electromechanics II A continuum model of cartilage electrokinetics and correlation with experiments J Biomech 20: 629 639 Freed, LE, Marquis, JC, Nohria, A, Emmanual, J, Mikos, AG, Langer, R (1993) Neocartilage formation in vitro and in vivo using cells cultured on synthetic biodegradable polymers J Biomed Mater Res 27: 11 23 Freed, LE, Grande, DA, Lingbin, Z.

Suppose that we are given a sample sequence from a Bernoulli( ) process What are the regularities or deviations from randomness in this sequence One way to address the question is to nd the Kolmogorov complexity K(x n |n), which we discover to be roughly nH0 ( ) + log n + c Since, for = 1 , this is much less than n, we conclude that x n has structure 2 and is not randomly drawn Bernoulli( 1 ) But what is the structure The 2 rst attempt to nd the structure is to investigate the shortest program p for x n But the shortest description of p is about as long as p itself; otherwise, we could further compress the description of x n , contradicting the minimality of p So this attempt is fruitless.