Linear Complexity of Periodic Sequences Obtained from GF(q) sequences with Period q^n-1 by One-Symbol Insertion

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From a GF(q) sequence {a_i}_<i≧0> with Period q^n -1 we can obtain new periodic sequences {a^^^_i}_<i≧0> with period q^n by inserting one symbol b∈GF(q) at the end of each period.Let b_0 =Σ^<q^n-2>_<i=0>a_i.It is first shown that the linear complexity of {a^^^_i}_<i≧0>, denoted as LC({a^^^_i}), satisfies LC({a^^^_i}) = q^n if b≠-b_o and LC({a^^^_i}) ≦ q^n - 1 if b = -b_o. Most of known sequences are shown to satisfy the zero sum property,i.e., b_o = 0. For such sequences satisfying b_o = 0 it is shown that q^n - LC({a_i}) ≦ LC({a^^^_i}) ≦ q^n - 1 if b = 0.
社団法人電子情報通信学会の論文
1996-10-25