Generalizations of the bch bound

Author: wngo

August undefined, 2024

WebWe propose a bound, whose computational complexity is polynomial bounded,which is a generalization of the Hartmann-Tzeng bound and the Betti-Sala bound. In the majority of computed cases, our bound is the tightest among all known polynomial-time bounds, including the Roos bound. Keywords: Cyclic codes, DFT, BCH bound, Hartmann-Tzeng … WebGeneralizations of the BCH bound Information and Control 10.1016/s0019-9958(72)90887-x 1972 Vol 20 (5) pp. 489-498 Cited By ~ 86 Author(s): C.R.P. Hartmann K.K. Tzeng Keyword(s): Bch Bound Download Full-text Decoding binary expansions of low-rate Reed-Solomon codes far beyond the BCH bound

Spectral Method for Quasi-Cyclic Code Analysis - INFONA

WebAbstract The tensor product of one code endowed with the Hamming metric and one endowed with the rank metric is analyzed. This gives a code which naturally inherits the sum-rank metric. Specializin... WebDec 1, 2024 · Polycyclic codes are a powerful generalization of cyclic and constacyclic codes. Their algebraic structure is studied here by the theory of invariant subspaces from linear algebra. As an application, a bound on the minimum distance of these codes is derived which outperforms, in some cases, the natural analogue of the BCH bound. portal of exit for lyme disease

New bounds on the minimum distance of cyclic codes

WebJun 1, 2024 · Out of the most famous bounds, we can certainly find the BCH [5], [4], [13], the Hartmann-Tzeng (HT) [12] and the Roos bound [31], [30]. More recently, generalizations of these types of bounds have been proposed by embedding the code into a cyclic product code; see [32]. WebTwo generalizations of the Hartmann-Tzeng (HT) bound on the minimum distance of q-ary cyclic codes are proposed and it is shown that unique decoding up to this bound is always possible and outline a quadratic-time syndrome-based error decoding algorithm. WebWe propose a bound, whose computational complexity is polynomial bounded,which is a generalization of the Hartmann-Tzeng bound and the Betti-Sala bound. In the … portal of exit of chickenpox

Spectral Method for Quasi-Cyclic Code Analysis - INFONA

Generalizations of the BCH Bound Semantic Scholar

WebBCH Bound Theorem (Bose–Chaudhuri–Hocquenghem Bound, 1959/60) given [n,k,d] q cyclic code Cwith D C three integers f, m and δwith m 6= 0 , gcd(n,m) = 1 and δ≥2, s.t.: {0,m,2m,...,(δ−2)m}⊆D(f) C. Then d ≥d∗ BCH def= δ. Example: Binary Cyclic Code of Length 17 We consider again the [17,9,5]2 cyclic code Cwith deﬁning set: D WebThe computation of the minimum distance of a cyclic code, or a lower bound for it, is one of the main problems on abelian codes (see, for example, [3, 6, 7]). The oldest lower bound for the minimum distance of a cyclic code is the BCH bound [5, p. 151]. The study of this bound and its generalizations is a classical topic which irt device dr john finneyWebSep 26, 2012 · Spectral Method for Quasi-Cyclic Code Analysis Abstract: A generalization of the BCH bound to the case of quasi-cyclic codes is proposed. The new approach is based on eigenvalues of matrix polynomials. This results in improved minimum distance estimates compared to the existing bounds. portal of exit for ringworm

"WebMay 1, 2014 · A new bound on the minimum distance of q-ary cyclic codes is proposed. It is based on the description by another cyclic code with small minimum distance. The connection to the BCH bound and the Hartmann---Tzeng (HT) bound is formulated explicitly. We show that for many cases our approach improves the HT bound. " - Generalizations of the bch bound

Generalizations of the bch bound

Sum-rank product codes and bounds on the minimum distance

http://www-math.mit.edu/~djk/18.310/Lecture-Notes/properties_bch_codes.html WebA statistical decoding of simultaneous burst and random errors beyond the BCH bound using reed-solomon codes Electronics and Communications in Japan (Part III …

Did you know?

WebGeneralizations of the BCH bound Information and Control 10.1016/s0019-9958 (72)90887-x 1972 Vol 20 (5) pp. 489-498 Cited By ~ 86 Author (s): C.R.P. Hartmann K.K. Tzeng Keyword (s): Bch Bound Download Full-text Computing the Camion's multivariate BCH bound 2013 IEEE Information Theory Workshop (ITW) 10.1109/itw.2013.6691285 … WebA generalization of the BCH bound to the case of quasi-cyclic codes is proposed. The new approach is based on eigenvalues of matrix polynomials. This results in improved …

WebNov 30, 2024 · The second bound also uses a second cyclic code, namely the non-zero-locator code, but is not directly related to cyclic product codes and it generalizes a special case of the Roos bound. ... C. Roos, A generalization of the BCH bound for cyclic codes, including the Hartmann-Tzeng bound, J. Combin. Theory Ser. A, 33 (1982), 229-232. …

WebJul 20, 2012 · A new bound on the minimum distance of q-ary cyclic codes is proposed. It is based on the description by another cyclic code with small minimum distance. The connection to the BCH bound and the Hartmann–Tzeng (HT) bound is formulated explicitly. We show that for many cases our approach improves the HT bound. Furthermore, we … WebSep 1, 1982 · A generalization of the BCH bound for cyclic codes, including the Hartmann-Tzeng bound - ScienceDirect Journal of Combinatorial Theory, Series A Volume 33, …

WebMar 13, 2024 · Adobe Premiere Pro 2024 is an excellent application which uses advanced stereoscopic 3D editing, auto color adjustment and the audio keyframing features to help you create amazing videos from social to the big screen.

WebA new bound on the minimum distance of q-ary cyclic codes is proposed. It is based on the description by another cyclic code with small minimum distance. The connection to the … portal of exit of german measlesWebJan 1, 2005 · To illustrate the power of this approach, a slight generalization of the Hartmann-Tzeng lower bound on minimum distance is proved, as well as the Bose-Chaudhuri-Hocquenghem lower bound. Other applications of linear complexity in the theory of cyclic codes are indicated. irt deadliest roadsWebHartmann, C.R.P., Tzeng, K.K.: Generalizations of the BCH bound. Information and Control 20, 489–498 (1972) CrossRef MathSciNet MATH Google Scholar Roos, C.: A generalization of the BCH bound for cyclic codes, including the Hartmann-Tzeng bound. Journal of Combinatorial Theory Ser. A 33, 229–232 (1982) irt distribution bloemfonteinWebNov 17, 2024 · There are generalizations of the BCH bound which may be sometimes applied. I don't know of any constructive way that will work in general. See. C Roos, A generalization of the BCH bound for cyclic codes, including the Hartmann-Tzeng bound, Journal of Combinatorial Theory, Series A, 33(2):1982. which is available here. irt distribution pty ltdWebUnder these assumptions, a generalization bound is a theorem, which holds for any distribution and states that, with high probability, applying the learning algorithm to a … irt deadliest roads onlineWebHartmann,C.,Tzeng,K.: Generalizations of the BCH bound,InformationandControl20(5),489– 498(1972) [Roos] Roos, C.: A generalization of the BCH bound for cyclic codes, … portal of glory edmontonWebSep 26, 2016 · This is our first generalization bound, it states that the generalization error is bounded by the training error plus a function of … irt digital analytics