The problem of mimicking the concertina locomotion mode of biological snakes through narrow channels of uncertain width, using a multi-link planar serpenoid robot, is considered. A novel algorithm for generating a reference trajectory that accurately reproduces this natural gait pattern is proposed and analysed for straight channels. A modification of this algorithm leverages feedback from the joints' currents and angular velocities to dynamically adjust the robot's movements within channels of unknown and varying widths. Experiments through rugged artificial channels of varying width show remarkable ability of the programmed snake robot to negotiate such terrains with agility and reasonable speed.

In this paper, we consider the problem of determining the weight spectrum ofq-ary codesC(3,m) associated with Grassmann varietiesG(3,m). Form=6, this was done in a paper by Nogin in 1997. We derive a formula for the weight of a codeword ofC(3,m), in terms of certain varieties associated with alternating trilinear forms on Fqm. The classification of such forms under the action of the general linear groupGL(m, Fq) is the other component that is required to calculate the spectrum ofC(3,m). Form=7, we explicitly determine the varieties mentioned above. The classification problem for alternating three-forms on Fq7was solved in a study by Cohen and Helminck in 1988, which we then use to determine the spectrum ofC(3,7).

Given a primitive polynomial$p(x)$, of degree$n$, we deal with the problem of finding the number of possible linear feedback shift register realizations, with m-input m-output delay elements, such that the corresponding characteristic polynomial is$p(x)$. We show the equivalence between these realizations and a set of specially structured matrices. Furthermore, the number of realizations is computed for some special cases.