Abstract In this article, constant dimension subspace codes whose codewords have subspace distance in a prescribed set of integers, are considered. The easiest example of such an object is a junta (Combin Probab Comput 18(1–2):107–122, 2009); i.e. a subspace code in which all codewords go through a common subspace. We focus on the case when only two intersection values for the codewords, are assigned. In such a case we determine an upper bound for the dimension of the vector space spanned by the elements of a non-junta code. In addition, if the two intersection values are consecutive, we prove that such a bound is tight, and classify the examples attaining the largest possible dimension as one of four infinite families.

Let Cn−1(n,q) be the code arising from the incidence of points and hyperplanes in the Desarguesian projective space PG(n,q). Recently, Polverino and Zullo (J Comb Theory Ser A 158:1–11, 2018) proved that within this code, all non-zero code words of weight at most 2qn−1 are scalar multiples of either the incidence vector of one hyperplane, or the difference of the incidence vectors of two distinct hyperplanes. We prove that all code words of weight at most (4q−O(q√))qn−2 are linear combinations of incidence vectors of hyperplanes through a common (n−3)-space. This extends previous results for large values of q.

In 1991, C.L. Chen used the inverted construction Y/sub 1/ on binary linear codes of minimum Hamming distance five to construct a new [47, 36, 5] code. We examine this construction in depth and show that no such codes are obtained unless the fields GF(8) or GF(32) are used. Using MAGMA, we prove that the binary [11, 4, 5] code and the binary [15, 7, 5] extension found by Chen are the only possible such codes using the field GF(8); indeed, the latter is a Bose-Chaudhuri-Hocquenghem (BCH) code. We prove also that, using the field GF(32), precisely three nonequivalent binary [47, 36, 5] codes arise along with one extension to a [63, 51, 5] code.