We prove that for $n$ sufficiently large, all perfect 3-hash linear codes in notation="LaTeX">$\mathbb {F}_{3}^{n}$ must have dimension at most notation="LaTeX">$\left ({\frac {1}{4}-\epsilon }\right)n$ some absolute constant notation...

Linear code with complementary dual(LCD) are those codes which meet their duals trivially. In this paper we will give rather alternative proof of Massey’s theorem[8], which is one of the most important characterization of LCD codes. Let LCD[n, k]3 denote the maximum of possible values of d among [n, k, d] ternary codes. We will give bound on LCD[n, k]3. We will also discuss the cases when this ...

This paper studies and classifies linear transformations that connect Hamming distances of codes. These include irreducible linear transformations and their concatenations. Their effect on the Hamming weights of codewords is also studied. Both linear and non-linear codes over fields are considered. We construct a family of pure binary quantum codes using these transformations. It is shown that ...