On Gilbert-Varshamov type bounds for Z2k linear codes
نویسندگان
چکیده
In this paper we derive a Gilbert-Varshamov type bound for linear codes over Galois rings GR(pl; j): However, this bound does not guarantee existence of better linear codes over GR(pl; j) than the usual Gilbert-Varshamov bound for linear codes over the residue class field GR(pj): Next we derive a Gilbert-Varshamov type bound for Z4 linear codes which guarantees the existence of Z4 linear codes reaching the usual Gilbert-Varshamov bound for binary codes. Finally we derive a Gilbert-Varshamov type bound for Z2k linear codes.
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