New Sufficient Existence Conditions for Codes Meeting the Varshamov–Greismer Bound

For any value of the dimension, and for any upper bound on the weights of the code vectors, the author defines the class of generating matrices of binary linear optimal anticodes. Permissible lower bounds are obtained on the maximum number of repetitions of a column in matrices from the class introduced, and, as a consequence, new sufficient existence conditions are obtained for codes that meet the Varshamov–Greismer bound.