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Alice selects a binary (n, k)-linear Goppa code, G, capable of correcting t errors. This code possesses an efficient decoding algorithm. Alice generates a (n − k) × n parity check matrix, H, for the code, G. Alice selects a random (n − k) × (n − k) binary non-singular matrix, S. Alice selects a random n × n permutation matrix, P.
Flood routing is a procedure to determine the time and magnitude of flow (i.e., the flow hydrograph) at a point on a watercourse from known or assumed hydrographs at one or more points upstream. The procedure is specifically known as Flood routing, if the flow is a flood. [14] [15] After Routing, the peak gets attenuated & a time lag is ...
Code-excited linear prediction (CELP) is a linear predictive speech coding algorithm originally proposed by Manfred R. Schroeder and Bishnu S. Atal in 1985. At the time, it provided significantly better quality than existing low bit-rate algorithms, such as residual-excited linear prediction (RELP) and linear predictive coding (LPC) vocoders (e.g., FS-1015).
Given a prime number q and prime power q m with positive integers m and d such that d ≤ q m − 1, a primitive narrow-sense BCH code over the finite field (or Galois field) GF(q) with code length n = q m − 1 and distance at least d is constructed by the following method.
Several such algorithms exist, such as going through each codeword of the code, syndrome decoding, or information set decoding. Decoding a general linear code, however, is known to be NP-hard , [ 3 ] however, and all of the above-mentioned methods have exponential running time.
Tanner proved the following bounds Let be the rate of the resulting linear code, let the degree of the digit nodes be and the degree of the subcode nodes be .If each subcode node is associated with a linear code (n,k) with rate r = k/n, then the rate of the code is bounded by
While the basic algorithm is a linear interpolation sort, if the input distribution is known to be non-uniform, a non-linear division will more closely approximate this ideal. Likewise, the final sort can use any of a number of techniques, including a recursive flash sort.
More precisely, the source coding theorem states that for any source distribution, the expected code length satisfies [(())] [ (())], where is the number of symbols in a code word, is the coding function, is the number of symbols used to make output codes and is the probability of the source symbol. An entropy coding attempts to ...