Distance-Regular Graphs

/pdf/handbook-of-magma-functions-5anhrdxxj3.pdf

Handbook of magma functions

One formidable difficulty in quantum communication and computation is to protect information-carrying quantum states against undesired interactions with the environment. To address this difficulty, many good quantum error-correcting codes have been derived as binary stabilizer codes. Fault-tolerant quantum computation prompted the study of nonbinary quantum codes, but the theory of such codes is not as advanced as that of binary quantum codes. This paper describes the basic theory of stabilizer codes over finite fields. The relation between stabilizer codes and general quantum codes is clarified by introducing a Galois theory for these objects. A characterization of nonbinary stabilizer codes over Fq in terms of classical codes over Fq 2 is provided that generalizes the well-known notion of additive codes over F4 of the binary case. This paper also derives lower and upper bounds on the minimum distance of stabilizer codes, gives several code constructions, and derives numerous families of stabilizer codes, including quantum Hamming codes, quadratic residue codes, quantum Melas codes, quantum Bose-Chaudhuri-Hocquenghem (BCH) codes, and quantum character codes. The puncturing theory by Rains is generalized to additive codes that are not necessarily pure. Bounds on the maximal length of maximum distance separable stabilizer codes are given. A discussion of open problems concludes this paper

Nonbinary Stabilizer Codes Over Finite Fields

Laplacian energy of a graph

On a Problem in Combinations

Algebraic Combinatorics and Applications : Proceedings

Let F n be a vector space of dimension n over the finite field Fq. A q-analog of a Steiner system (briefly, a q-Steiner system), denoted Sq(t,k,n), is a set S of k-dimensional subspaces of Fn such that each t-dimensional sub- space of F n is contained in exactly one element of S. Presently, q-Steiner systems are known only for t = 1, and in the trivial cases t = k and k = n. In this paper, the first nontrivial q-Steiner systems with t > 2 are constructed. Specifically, several nonisomorphic q-Steiner systems S2(2,3,13) are found by requiring that their automorphism groups contain the normalizer of a Singer subgroup of GL(13,2). This approach leads to an instance of the exact cover problem, which turns out to have many solutions.

/pdf/existence-of-q-analogs-of-steiner-systems-16ezj5n4h0.pdf

EXISTENCE OF q-ANALOGS OF STEINER SYSTEMS

The purpose of this study was to determine the effect of below-knee compression stockings on running performance in men runners. Using a within-group study design, 21 moderately trained athletes (39.3 ± 10.9 years) without lower-leg abnormities were randomly assigned to perform a stepwise treadmill test up to a voluntary maximum with and without below-knee compressive stockings. The second treadmill test was completed within 10 days of recovery. Maximum running performance was determined by time under load (minutes), work (kJ), and aerobic capacity (ml·kg-1·min-1). Velocity (km·h-1) and time under load were assessed at different metabolic thresholds using the Dickhuth et al. lactate threshold model. Time under load (36.44 vs. 35.03 minutes, effect size [ES]: 0.40) and total work (422 vs. 399 kJ, ES: 0.30) were significantly higher with compression stockings compared with running socks. However, only slight, nonsignificant differences were observed for [latin capital V with dot above]o2max (53.3 vs. 52.2 ml·kg-1·min-1, ES: 0.18). Running performance at the anaerobic (minimum lactate + 1.5 mmol·L-1) threshold (14.11 vs. 13.90 km·h-1, ES: 0.22) and aerobic (minimum lactate + 0.5 mmol·L-1) thresholds (13.02 vs. 12.74 km·h-1, ES: 0.28) was significantly higher using compression stockings. Therefore, stockings with constant compression in the area of the calf muscle significantly improved running performance at different metabolic thresholds. However, the underlying mechanism was only partially explained by a slightly higher aerobic capacity.

Effect of compression stockings on running performance in men runners.

Error-Correcting Linear Codes: Classification by Isometry and Applications (Algorithms and Computation in Mathematics)

One of the main problems of subspace coding asks for the maximum possible cardinality of a subspace code with minimum distance at least $d$ over $\mathbb{F}_q^n$, where the dimensions of the codewords, which are vector spaces, are contained in $K\subseteq\{0,1,\dots,n\}$. In the special case of $K=\{k\}$ one speaks of constant dimension codes. Since this (still) emerging field is very prosperous on the one hand side and there are a lot of connections to classical objects from Galois geometry it is a bit difficult to keep or to obtain an overview about the current state of knowledge. To this end we have implemented an on-line database of the (at least to us) known results at \url{this http URL}. The aim of this recurrently updated technical report is to provide a user guide how this technical tool can be used in research projects and to describe the so far implemented theoretic and algorithmic knowledge.

Alfred Wassermann

Papers

Algebraic Combinatorics and Applications : Proceedings

EXISTENCE OF q-ANALOGS OF STEINER SYSTEMS

Effect of compression stockings on running performance in men runners.

Error-Correcting Linear Codes: Classification by Isometry and Applications (Algorithms and Computation in Mathematics)

Tables of subspace codes