A cyclic code is associated with another cyclic code to bound its minimum distance. The algebraic relation between these two codes allows the formulation of syndromes and a key equation. In this contribution, we outline the decoding approach for the case of errors and erasures and show how the Extended Euclidean Algorithm can be used for decoding.

Reference counting is a widely employed memory management technique, in which garbage collection operations are interleaved with computation. Standard reference counting has the major drawback of being unable to handle cyclic structures. This paper presents an important optimisation to a recently published algorithm for cyclic reference counting. Proofs of the correctness of the original and la...

We consider a class of 3-error-correcting cyclic codes of length 2−1 over the two-element field F2. The generator polynomial of a code of this class has zeroes α, α i +1 and α j , where α is a primitive element of the field F2m . In short, {1, 2+1, 2 +1} refers to the zero set of these codes. Kasami in 1971 and Bracken and Helleseth in 2009, showed that cyclic codes with zeroes {1, 2 + 1, 2 + 1...

An algorithm for traversing binary trees in linear time using constant extra space is presented. The algorithm offers advantages to both Robson traversal and Lindstrom scanning. Under certain conditions, the algorithm can be applied to the marking of cyclic list structures. The algorithm can be generalized to handle N-trees and N-lists.

This paper investigates finite-horizon optimal control problem of completely unknown discrete-time linear systems. The here refers to that the system dynamics are unknown. Compared with infinite-horizon control, Riccati equation (RE) is time-dependent and must meet certain terminal boundary constraints, which brings greater challenges. Meanwhile, have also caused additional main innovation this...

We present an n-processor and O(lo~n)-time parallel RAM algorithm for finding a depth-first-search tree in an n·vertex planar graph. The algorithm is based on a new n-processor algorithm for finding a cyclic separator in a planar graph and Smith's original parallel depth-first-search algorithm for planar graphs [Smi86].

in this study, a researching program is conducted by cyclic triaxial test to determine the post-cyclic behavior of bushehr carbonate sand retrieved from the north of the persian gulf, under anisotropic consolidation at 200 kpa confining pressure. the article compares the post-cyclic monotonic strength and excess pore water pressures generated after the test with the pre-cyclic monotonic results...

Almwct--Two new computationally efficient afgorithms are developed for fmdiug tke exact burst-comxtiug limit of a cyclic code. The first algorithm is based on testing tbe culumn rank of certain submatrices of the parity& matrix of the code. Aa auxiliary result is a proof that every cyclic (n,k) code, with a min immu distauce of at least three, CorrecQ at least all bursts of length L(n-2k+l)/2J ...

In this paper, a robust cyclic ADC architecture with βencoder is proposed and circuit scheme using switched-capacitor (SC) circuit is introduced. Different from the conventional binary ADC, the redundancy of proposed cyclic ADC outputs β-expansion code and has an advantage of error correction. This feature makes ADC robust against the offset of comparator capacitor mismatch and finite DC gain o...

In this paper we adress a new cyclic problem: finding periodic schedules for unitary resource constrained cyclic scheduling problem. Such resource constraints are characterized by k, the number of types of functional units employed and mx the maximal number of processors of the same type. The main problem is to cope with both precedence delays and resources which make the problem NP-complete in...