On ( 1 − um ) - Cyclic Codes over F 2 + uF 2 + u 2 F 2 + u 3 F
نویسنده
چکیده
A new Gray map between codes over F2 +uF2 +uF2 +uF2 + ....+ uF2 and codes over F2 is defined. It is proved that the Gray image of a linear (1− um)-cyclic code over F2 + uF2 + uF2 + uF2 + .... + uF2 of length n is a binary distance invariant quasi-cylic code of index 2m−1 and length 2mn. It is also proved that if n is odd, then every code of length 2mn over F2 which is the Gray image of a linear cyclic code of length n over F2 + uF2 + uF2 + uF2 + .... + uF2 is equivalent to a quasi-cyclic code of index 2m−1. Mathematics Subject Classification: 94B15, 94B60
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