Synthesizing All Linearized Shift-Registers of the Minimal or Required Length

Konferenz: SCC'10 - 8th International ITG Conference on Source and Channel Coding
18.01.2010 - 21.01.2010 in Siegen, Germany

Tagungsband: SCC'10

Seiten: 6Sprache: EnglischTyp: PDF

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Sidorenko, Vladimir R.; Bossert, Martin (Inst. of Telecommunications and Applied Information Theory, Ulm University, Ulm, Germany)

An efficient algorithm synthesizing all q-linearized shift-registers of the minimal or required length generating a sequence of length N over a finite field Fqm is considered. This algorithm, which is a generalization of the Berlekamp-Massey algorithm, has time complexity O(N(exp2)) operations in Fqm, and can be applied for efficient solving the key equation when decoding Gabidulin codes up to and beyond half the minimum rank distance.