Decoding of Cyclic Codes over F 2 + Uf 2
نویسندگان
چکیده
1 Abstract We give a simple decoding algorithm to decode linear cyclic codes of odd length over the ring R = F2 + uF2 = f0; 1; u; u = u + 1g, where u 2 = 0. A spectral representation of the cyclic codes over R is given and a BCH like bound is given for the Lee distance of the codes. The ring R shares many properties of Z4 and F4 and admits a linear \Gray map". 1 0 1 u u u 0 u 1 u u 0 u u 0 + 0 1 u u 0 0 1 u u 1 1 0 u u u u u 0 1 u u u 1 0 Table 1: Multiplication and addition tables for the ring F 2 + F 2 .
منابع مشابه
Cyclic Codes and Self-Dual Codes Over F2 + uF2
We introduce linear cyclic codes over the ring F 2 + uF 2 = f0; 1; u; u = u + 1g, where u 2 = 0. This ring shares many properties of Z 4 and F 4 and admits a linear "Gray map". Cyclic codes are described as modules over (F 2 + uF 2) n which may not be free. Self-dual codes of odd length exists as in the case of Z 4-codes. We exhibit some extremal codes of this very interesting family.
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