科研之友
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摘要
Let R = F-2m + uF(2m) + ... + ukF(2m), where F-2m is the finite field with 2(m) elements, m is a positive integer, and u is an indeterminate with u(k+1) = 0. In this paper, we propose the constructions of two new families of quantum codes obtained from dual-containing cyclic codes of odd length over R. A new Gray map over R is defined, and a sufficient and necessary condition for the existence of dual-containing cyclic codes over R is given. A new family of 2(m)-ary quantum codes is obtained via the Gray map and the Calderbank-Shor-Steane construction from dual-containing cyclic codes over R. In particular, a new family of binary quantum codes is obtained via the Gray map, the trace map and the Calderbank-Shor-Steane construction from dual-containing cyclic codes over R.
