Geometric Conditions for the Extendability of Ternary Linear Codes

Abstract

We give the necessary and sufficient conditions for the extendability of ternary linear codes of dimension k, 4 ≤k ≤6, with minimum distance d ≡1 or 2 (mod 3) from a geometrical point of view. We also give the necessary and sufficient conditions for the extendability of ternary linear codes with diversity (θ _{k − − 2},3^{k − − 2}), (θ _{k − − 2}+3^{k − − 3},4 3^{k − − 3}), (θ _{k − − 2}–3^{k − − 3},53^{k − − 3}) for k ≥6, where θ _j = (3^j + 1–1)/2.