In this paper, we propose primitive rateless (PR) codes. A PR code is characterized by the message length and a polynomial over $\mathbf{GF}(2)$, which can generate potentially limitless number of coded symbols. We show that codewords truncated at any arbitrary be represented as subsequences maximum-length sequence ($m$-sequence). characterize Hamming weight distribution codes their duals for p...

A point in the d-dimensional integer lattice Z d $\mathbb {Z}^d$ is primitive when its coordinates are relatively prime. Two points multiples of one another they opposite, and for this reason, we consider half within lattice, ones whose first non-zero coordinate positive. We solve packing problem that asks largest possible number such absolute values any given sum to at most a fixed k. present ...