We transpose the theory of rank metric. Gabidulin codes (8) W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes. Cambridge. Leech's construction is based on the binary Golay code of length. 24. Later on (13) V.Pless, An Introduction to the Theory of Error-Correcting Codes, Wi. Download full text in PDF Opens in a new window. R. Brualdi and V. Pless, On the length of codes with a given covering radius, Preprint. Introduction to the Theory of Functions of One VariableA. Characterization of (2(q + 1) + 2, 2, t, q)-min-hyper in PG(t, q) (t 3, q 5) and its applications to error-correcting codes. of Coding Theory. 5. 1.

http://ieeexplore.ieee.org/iel5/5/31339/01457228.pdf

Introduction to the theory of error-correcting codes

Design optimization for reliable networking is necessary for Ethernet ring mesh networks with ITU-T G.8032 Ethernet ring protection recommendation or with the IEC 62439-3 high-availability seamless redundancy protocol. To achieve this goal, the precise analysis of reliability/availability in Ethernet ring mesh consisting of single or multiple rings is one of the basic needs. Calculation of network reliability in these networks is an NP-hard problem. Therefore, most of the reliability and availability analyses were based on approximation and inaccurate methods. In this paper, at first, using decomposition method, a careful reliability analysis of Ethernet single-ring mesh networks will be presented. In addition, an accurate analysis of the reliability of Ethernet multiple-ring mesh networks will be performed by a novel approach named the spanning tree set method. Then, the availability of the ring networks with imperfect coverage and online repair assumptions will be analyzed using a hierarchical model in which each subsystem is modeled as a series system of independent Markov components.

Reliability Analysis of Ethernet Ring Mesh Networks

The aim of this paper is to present a recursive construction of simple t-designs for arbitrary t. The construction is of purely combinatorial nature and it requires finding solutions for the indices of the ingredient designs that satisfy a certain set of equalities. We give a small number of examples to illustrate the construction, whereby we have found a large number of new t-designs, which were previously unknown. This indicates that the method is useful and powerful.

Simple t-designs: a recursive construction for arbitrary t

In this paper we investigate simple t-designs having s-resolutions for $$t \ge 3$$
 and $$1 \le s <t$$
 . The study focuses particularly on recursive construction methods for these designs. One of the results, viewed as the main theorem, presents a general and effective method for finding s-resolvable t-designs, and it also yields statements about large sets of s-designs as by-products. As an example, we show the construction of a 3-resolvable infinite family of simple 4-designs with parameters 4-
 $$(2^n+2,7, 70(2^n-2)/3)$$
 , $$\gcd (n,6)=1$$
 , $$n \ge 5$$
 .

Recursive constructions for s-resolvable t-designs

This work presents a recursive construction for simple $t$-designs using resolutions of the ingredient designs. The result extends a construction of $t$-designs in our recent paper [39]. Essentially, the method in [39] describes the blocks of a constructed design as a collection of block unions from a number of appropriate pairs of disjoint ingredient designs. Now, if some pairs of these ingredient $t$-designs have both a suitable $s$-resolution, then we can define a distance mapping on their resolution classes. Using this mapping enables us to have more possibilities for forming blocks from those pairs. The method makes it possible for constructing many new simple $t$-designs. We give some application results of the new construction.

A recursive construction for simple $t$-designs using resolution

Some new large sets of t-designs

Let nq(k;d) denote the smallest value of n for which there exists a linear (n;k;d)-code over the Galois eld GF (q). An (n;k;d)-code whose length is equal to nq(k;d) is called optimal. In this paper we present some matrix generators for the family of optimal (n; 3;d) codes over GF (7) and GF (11). Most of our given codes in GF (7) are non- isomorphic with the codes presented before. Our given codes in GF (11) are all new.

/pdf/optimal-linear-codes-over-gf-7-and-gf-11-with-dimension-3-d4wi7jmfsk.pdf

Optimal Linear Codes Over GF(7) and GF(11) with Dimension 3

A t-regular self-complementary k-hypergraph, denoted by $$\hbox {SRHG}(t,k,v)$$
 , is a k-hypergraph with a v-set V as vertex set and an edge set E, such that every t-subset of V lies in the same number of edges and there is a permutation $$\sigma \in S_v $$
 with the property that $$e\in E$$
 if and only if $$\sigma (e)\notin E$$
 . It is clear that a set of trivial necessary conditions for the existence of an $$\hbox {SRHG}(t,k,v)$$
 is that $${v-i\atopwithdelims ()k-i}$$
 is an even integer for all $$i=0,1,...,t$$
 . In this paper, we extend the method of partitionable sets for constructing large sets of t-designs to obtain new $$\hbox {SRHG}(t,k,v)$$
 . In particular, we present $$\hbox {SRHG}(2,3,10)$$
 , $$\hbox {SRHG}(2,4,10)$$
 , $$\hbox {SRHG}(2,4,11)$$
 and $$\hbox {SRHG}(2,5,10)$$
 . Also we show that the trivial necessary conditions for the existence of $$\hbox {SRHG}(2,k,v)$$
 with $$k\le 7$$
 are sufficient.

Some Infinite Families of t -Regular Self-complementary k -Hypergraphs

A New Proof of Cayleyʼs Formula for Labeled Spanning Trees

We use the recursive method of construction large sets of t-designs given by Qiu-rong Wu (A note on extending t-designs‎, ‎{em Australas‎ ‎J‎ ‎Combin}‎, ‎{bf 4} (1991) 229--235), and present a similar method for constructing $t$-subset-regular‎ ‎self-complementary $k$-uniform hypergraphs of order $v$‎ ‎As an‎ ‎application we show the existence of a new family of 2-subset-regular‎ ‎self-complementary 4-uniform hypergraphs with $v=16m+3$‎

http://toc.ui.ac.ir/article_20363_caa3ab087951b3985516a80dc389ee3a.pdf

M. Emami

Papers

Some new large sets of t-designs

Optimal Linear Codes Over GF(7) and GF(11) with Dimension 3

Some Infinite Families of t -Regular Self-complementary k -Hypergraphs

A New Proof of Cayleyʼs Formula for Labeled Spanning Trees

A family of $t$-regular self-complementary $k$-hypergraphs