The weight hierarchy of a linear [ n ; k ; q ] code C over GF ( q ) is the sequence ( d 1 , d 2 , ···, d k ) where d r is the smallest support of any r -dimensional subcode of C . “Determining all possible weight hierarchies of general linear codes” is a basic theoretical issue and has important scientific significance in communication system. However, it is impossible for q -ary linear codes of dimension k when q and k are slightly larger, then a reasonable formulation of the problem is modified as: “Determine almost all weight hierarchies of general q -ary linear codes of dimension k ”. In this paper, based on the finite projective geometry method, the authors study q -ary linear codes of dimension 5 in class IV, and find new necessary conditions of their weight hierarchies, and classify their weight hierarchies into 6 subclasses. The authors also develop and improve the method of the subspace set, thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV. It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes (classes III and VI), and break through the difficulties. Furthermore, the new necessary conditions show that original necessary conditions of the weight hierarchies of k -dimensional codes were not enough (not most tight nor best), so, it is important to excogitate further new necessary conditions for attacking and solving the k -dimensional problem.

The weight hierarchy of a [n, k; q] linear code C over F-q is the sequence (d(1),...,d(r),...,d(k)), where d(r) is the smallest support weight of an r-dimensional subcode of C. In this paper, by using the finite projective geometry method, we research a class of weight hierarchy of linear codes with dimension 5. We first find some new preconditions of this class. Then we divide its weight hierarchies into six subclasses, and research one subclass to determine nearly all the weight hierarchies of this subclass of weight hierarchies of linear codes with dimension 5.

A new conifer, Austrohamia acanthobractea, sp. nov., is described from the Jurassic Daohugou flora, Inner Mongolia Autonomous Region, China. The material consists of impressions represented by well-preserved leafy twigs and branches as well as ovulate cones. Leafy shoots with at least two orders of branching; ultimate branchlets alternate or sub-opposite with helically arranged leaves, decurrent at base with distal rounded tip; dorsiventrally flattened and univeined. Ovuliferous cones elliptical, less than 1 cm long, terminally borne on ultimate and penultimate branches, composed of helically arranged bracts with ovules disposed on their adaxial surfaces. The presence of similar, if not identical taxa, on both sides of the Pacific indicates the cosmopolitan distribution of primitive Cupressaceae between East Asia (Eurasia) and South America in the Pangaea.