WebOpen problems on cyclic codes Pascale Charpin Contents 1 Introduction 3 2 Di erent kinds of cyclic codes. 4 ... multiplication by q(mod n), such that any codeword x 2 Csatis es ˆs(x) = 0; 8s2 T : The set Tis a union of q-cyclotomic cosets modulo n; any s2 Tcorresponds to a zero of C, say s, (see Chapter 1, Section 4). WebMar 3, 2024 · Many optimal classical cyclic, constacyclic, repeated-root cyclic, skew-cyclic code, quasi-cyclic (QC), generalized QC codes, simplex codes etc. with good dual-containing properties have been given in recent years, and corresponding QECCs [ 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17] with good parameters are constructed based on them.
-double cyclic codes - Springer
WebJan 21, 2024 · The construction of new QECCs is a hot topic in recent decades [ 1, 9, 12, 14, 15, 21 ]. The quantum BCH codes were studied in many literatures [ 1, 14, 21 ]. In 2013, Kai et al. constructed some new quantum MDS codes from negacyclic codes. Recently, La Guardia constructed some new quantum codes from cyclic codes. Webs(X) = s0 +s1X + +sr 1Xr 1 is the current state polynomial The next state polynomial s0(X) is given by s0(X) = [aXr +Xs(X)] mod g(X) If the initial state polynomial is zero and the input … grace community church salida co
Cyclic Code - Properties with Example for Encoding and …
WebParity Check Matrix Now since a(x)b(x) ≡ 0 mod (xn - 1), the coefficient of each power of x must be 0. From the discussion above, this implies that ac = 0 (i.e., a and c are orthogonal) whenever c is any cyclic shift of the vector obtained from b … WebJul 25, 2024 · In this paper, we study the symbol-pair weight distribution of some irreducible cyclic codes. We define generalized cyclotomic numbers and provide some of their … WebMar 16, 2016 · From what I understood of it, a cyclic code is a special kind of linear code with the property that any codeword cyclic shift is also a codeword. Generally, we start with number of message bits k and number of code bits n in a codeword and then try to build a cyclic code with these requirements. chilled asparagus