On the Construction of Codes from an Asymptotically Good Tower over F8

In 2002, van der Geer and van der Vlugt gave explicit equations for an asymptotically good tower of curves over the field F8. In this paper, we will present a method for constructing Goppa codes from these curves as well as explicit constructions for the third level of the tower. The approach is to find an associated plane curve for each curve in the tower and then to use the algorithms of Haché and Le Brigand to find the corresponding Goppa codes.

Asymptotically-good, multigroup decodable space-time block codes

For a family of Space-Time Block Codes (STBCs) C-1, C-2,..., with increasing number of transmit antennas N-i, with rates R-i complex symbols per channel use, i = 1, 2,..., we introduce the notion of asymptotic normalized rate which we define as lim(i ->infinity) R-i/N-i, and we say that a family of STBCs is asymptotically-good if its asymptotic normalized rate is non-zero, i. e., when the rate scales as a non-zero fraction of the number of transmit antennas. An STBC C is said to be g-group decodable, g >= 2, if the information symbols encoded by it can be partitioned into g groups, such that each group of symbols can be ML decoded independently of the others. In this paper we construct full-diversity g-group decodable codes with rates greater than one complex symbol per channel use for all g >= 2. Specifically, we construct delay-optimal, g-group decodable codes for number of transmit antennas N-t that are a multiple of g2left perpendicular(g-1/2)right perpendicular with rate N-t/g2(g-1) + g(2)-g/2N(t). Using these new codes as building blocks, we then construct non-delay-optimal g-group decodable codes with rate roughly g times that of the delay-optimal codes, for number of antennas N-t that are a multiple of 2left perpendicular(g-1/2)right perpendicular, with delay gN(t) and rate Nt/2(g-1) + g-1/2N(t). For each g >= 2, the new delay-optimal and non-delay- optimal families of STBCs are both asymptotically-good, with the latter family having the largest asymptotic normalized rates among all known families of multigroup decodable codes with delay T <= gN(t). Also, for g >= 3, these are the first instances of g-group decodable codes with rates greater than 1 reported in the literature.

A family of asymptotically good lattices having a lattice in each dimension

A new constructive family of asymptotically good lattices with respect to sphere packing density is presented. The family has a lattice in every dimension n >= 1. Each lattice is obtained from a conveniently chosen integral ideal in a subfield of the cyclotomic field Q(zeta(q)) where q is the smallest prime congruent to 1 modulo n.

Asymptotically-Optimal, Fast-Decodable, Full-Diversity STBCs

For a family/sequence of Space-Time Block Codes (STBCs) C1, C2,⋯, with increasing number of transmit antennas Ni, with rates Ri complex symbols per channel use (cspcu), i = 1,2,⋯, the asymptotic normalized rate is defined as limi→∞ Ri/Ni. A family of STBCs is said to be asymptotically-good if the asymptotic normalized rate is non-zero, i.e., when the rate scales as a non-zero fraction of the number of transmit antennas, and the family of STBCs is said to be asymptotically-optimal if the asymptotic normalized rate is 1, which is the maximum possible value. In this paper, we construct a new class of full-diversity STBCs that have the least maximum-likelihood (ML) decoding complexity among all known codes for any number of transmit antennas N>;1 and rates R>;1 cspcu. For a large set of (R,N) pairs, the new codes have lower ML decoding complexity than the codes already available in the literature. Among the new codes, the class of full-rate codes (R=N) are asymptotically-optimal and fast-decodable, and for N>;5 have lower ML decoding complexity than all other families of asymptotically-optimal, fast-decodable, full-diversity STBCs available in the literature. The construction of the new STBCs is facilitated by the following further contributions of this paper: (i) Construction of a new class of asymptotically-good, full-diversity multigroup ML decodable codes, that not only includes STBCs for a larger set of antennas, but also either matches in rate or contains as a proper subset all other high-rate or asymptotically-good, delay-optimal, multigroup ML decodable codes available in the literature. (ii) Construction of a new class of fast-group-decodable codes (codes that combine the low ML decoding complexity properties of multigroup ML decodable codes and fast-decodable codes) for all even number of transmit antennas and rates 1 <; R ≤ 5/4.- - (iii) Given a design with full-rank linear dispersion matrices, we show that a full-diversity STBC can be constructed from this design by encoding the real symbols independently using only regular PAM constellations.

The implication of a term of good faith in commercial leases

Much has been written in the past decade on the subject of the implication of a term of good faith in contracts in Australia, particularly since the judgment Priestley JA in Renard Constructions (ME) Pty Ltd v Minister for Public Works (1992) 26 NSWLR 234. Except for an early article by Rachael Mulheron, 'Good Faith and Commercial Leases: New Opportunities for the Tenant' (1996) 4 APLJ 223, very little else has been written with respect to the possible application of the doctrine to the commercial leases.With the advent of two later New South Wales Supreme Court decisions Alcatel Australia Ltd v Scarcella (1998) 44 NSWLR 349 and, more recently, Advance Fitness v Bondi Diggers [1999] NSWSC 264, the question of the application of the doctrine in the commercial leasing context has been examined. This article briefly considers the nature and substance of the doctrine against the background of the relationship of lessor and lessee and examines in some depth the Australian decisions on commercial leases where it has been sought, unsuccessfully, to apply the doctrine. The article concludes by suggesting that as a standard commercial lease usually covers the field of agreement between lessor and lessee and as a lessee has a high degree of statutory protection derived from equitable principles, there may be little room for the operation of the doctrine in this legal environment.

The implication of a term of good faith in commercial leases — A brief response

By way of response to Professor Duncan's article,1 this article examines the theoretical basis for the implication of contractual terms, particularly the implication of a term at law. In this regard the recent decision of Barrett J in Overlook v Foxtel [2002] NSWSC 17 is considered, to the extent that it provides guidance concerning the implication of an obligation of good faith in the context of a commercial contract. A number of observations are made which may be considered likely to have application to the relationship of commercial landlord and tenant. The conclusion reached is that although the commercial landlord and tenant contractual relationship is highly regulated, this may not deny a remedy to a tenant who is the victim of a landlord's 'bad faith'. Finally, the article concludes by considering the extent to which it may be possible to contractually exclude the implied obligation of good faith.

Inter-agency working : good intentions and interaction dynamics

This paper explores inter-agency working and examines the implications of inter-agency operations for delivering multi-domain service outcomes. Cross-agency collaborative approaches to service delivery are suggested to provide the vehicle for achieving integrated service and policy goals. However, it is argued these need to be crafted ‘fit’ for purpose’ and may not be the requisite approach for all joint purposes. Moreover, some commentators suggest that the optimism about these partnership arrangements and cross-agency actions to resolve complex multi-dimensional problems may be misplaced and propose that further research into the actual rather than desired consequences of these arrangements may find that, at times, partnership working creates negative effects. While collaboration and partnerships are often framed as the way to achieve real breakthroughs in service delivery across agencies, there remain key challenges to interagency working. As more and insistent calls for agencies and other community actors to work together in resolving complex social problems are heeded, the implications of working across organizational boundaries need to be further investigated. This paper investigates cases of inter-agency programmes to understand the dimensions and limitations of inter-agency working. The paper concludes by offering a framework for better inter-agency working that has applicability across all sectors.