WebRead Cyclic Codes over Finite Fields. Read Cyclic Codes over Finite Fields. ScienceGate; Advanced Search; Author Search; Journal Finder; Blog; Sign in / Sign up; ScienceGate; ... WebSince every linear code is contained in an MDS linear code with the same minimum distance over some finite field extension, we focus our study on MDS linear codes. It is well-known that an MDS linear code with minimum distance 2 ℓ + 1 has an ℓ -error-correcting pair if and only if it is a generalized Reed-Solomon code.
(PDF) Skew cyclic Linear codes over 𝑹 = 𝑅 + 𝑤𝑅 + 𝑤2𝑅
WebA cyclic code has been one of the most active research topics in coding theory because they have many applications in data storage systems and communication systems. They have … WebThe Gray weight of the elements of R and a Gray map from Rn to Z2n 4 are defined, which lead to the MacWillams identity of the linear code ove r R, and the results show that there are no non-trivial MDS codes over R. In this paper, we study the linear codes over the commutative ring R = Z4 + vZ4, wherev2 = v. We define the Gray weight of the elements … diabetes statistics in north dakota
A class of minimal cyclic codes over finite fields
WebJan 6, 2024 · Minimal quadratic residue cyclic codes of length 2n. AbstractLetF be a finite field of prime power orderq (odd) and the multiplicative order ofq modulo 2n (n>1) be ϕ … WebIn this paper, we study minimal cyclic codes of length $$\ell ^{m}$$ ℓ m over a finite field $$\mathbb{F }_q$$ F q , where $$\ell $$ ℓ is a prime divisor of $$q-1 ... WebApr 1, 2024 · Kai and Zhu [29] later proposed a method for generating quantum codes using cyclic codes of odd length over the finite chain ring F 4 + v F 4 with u 2 = 0. Further, Qian [18] has introduced a method for generating quantum error-correcting codes using cyclic codes over the finite non-chain ring F 2 + v F 2 with arbitrary length v 2 = v. diabetes statistics in pennsylvania