BACKGROUND We intended to analyze the efficacy of a new integrated cage and plate device called Perfect-C for anterior cervical discectomy and fusion (ACDF) to cure single-level cervical degenerative disc disease. METHODS We enrolled 148 patients who were subjected to single-level ACDF with one of the following three surgical devices: a Perfect-C implant (41 patients), a Zero-P implant (36 pa...

Let C be a Z2Z4-additive code of length n > 3. We prove that if the binary Gray image of C, C = Φ(C), is a 1-perfect nonlinear code, then C cannot be a Z2Z4-cyclic code except for one case of length n = 15. Moreover, we give a parity check matrix for this cyclic code. Adding an even parity check coordinate to a Z2Z4-additive 1-perfect code gives an extended 1-perfect code. We also prove that an...

A binary extended 1-perfect code C folds over its kernel via the Steiner quadruple systems associated with its codewords. The resulting folding, proposed as a graph invariant for C, distinguishes among the 361 nonlinear codes C of kernel dimension κ obtained via Solov’eva-Phelps doubling construction, where 9 ≥ κ ≥ 5. Each of the 361 resulting graphs has most of its nonloop edges expressible in...

A binary extended 1-perfect code C folds over its kernel via the Steiner quadruple systems associated with its codewords. The resulting folding, proposed as a graph invariant for C, distinguishes among the 361 nonlinear codes C of kernel dimension κ obtained via Solov’eva-Phelps doubling construction, where 9 ≥ κ ≥ 5. Each of the 361 resulting graphs has most of its nonloop edges expressible in...

The idea of “forcing” has long been used in many research fields, such as colorings, orientations, geodetics and dominating sets in graph theory, as well as Latin squares, block designs and Steiner systems in combinatorics (see [1] and the references therein). Recently, the forcing on perfect matchings has been attracting more researchers attention. A forcing set of M is a subset of M contained...

The standard C/C++ implementation of a spatial partitioning data structure, such as octree and quadtree, is often inefficient in terms of storage requirements particularly when the memory overhead for maintaining parentto-child pointers is significant with respect to the amount of actual data in each tree node. In this work, we present a novel data structure that implements uniform spatial part...

the idea of “forcing” has long been used in many research fields, such as colorings, orientations, geodetics and dominating sets in graph theory, as well as latin squares, block designs and steiner systems in combinatorics (see [1] and the references therein). recently, the forcing on perfect matchings has been attracting more researchers attention. a forcing set of m is a subset of m contained...

The Krotov combining construction of perfect 1-error-correcting binary codes from 2000 and a theorem of Heden saying that every non-full-rank perfect 1-errorcorrecting binary code can be constructed by this combining construction is generalized to the q-ary case. Simply, every non-full-rank perfect code C is the union of a well-defined family of μ̄-components Kμ̄, where μ̄ belongs to an “outer” pe...

An (s; n; q; t)-perfect hash family is a set of functions 1 ; 2 ; : : :; s from a set V of cardinality n to a set F of cardinality q with the property that every t-subset of V is injectively mapped into F by at least one of the functions i. The paper shows that the maximum value n s;t (q) that n can take for xed s and t has a leading term that is linear in q if and only if t > s. Moreover, for ...