Abstract :
The authors extend to the q-ary case the notions of a normal code, a subnormal code, and the amalgamated direct sum construction, in order to investigate problems related to the covering radius of codes. For example, the authors prove that every nonbinary nontrivial perfect code is absubnormal. They also include some linear-programming lower bounds on ternary codes with covering radius 2 or 3
Keywords :
error correction codes; amalgamated direct sum construction; covering radius; linear-programming lower bounds; nonbinary nontrivial perfect code; normal code; q-ary codes; subnormal code; ternary codes; Error correction codes; Galois fields; Hamming distance; Linear code; Linear programming; Mathematics; Upper bound;
