On the Hamming distance of linear codes over a finite chain ring

@article{Norton2000OnTH,
  title={On the Hamming distance of linear codes over a finite chain ring},
  author={Graham H. Norton and Ana Salagean},
  journal={IEEE Trans. Information Theory},
  year={2000},
  volume={46},
  pages={1060-1067}
}
Let R be a finite chain ring (e.g. a Galois ring), K its residue field and C a linear code over R. We prove that d(C), the Hamming distance of C, is d((C : α)), where (C : α) is a submodule quotient, α is a certain element of R and denotes the canonical projection to K. These two codes also have the same set of minimal codeword supports. We explicitly construct a generator matrix/polynomial of (C : α) from the generator matrix/polynomials of C. We show that in general d(C) ≤ d(C) with equality… CONTINUE READING
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