Abstract
A Galois field GF(q m) can be regarded as a linear vector space over GF(q). The elements of GF(q m can be represented by m-tuples of elements belonging to GF(q). In this way, a sequence over GF(q m) becomes a sequence over GF(q). We call the sequence over GF(q) a mapping sequence. A change of basis of GF(q m) over GF(q) can change the period, the linear span and the autocorrelation function of a mapping sequence. The aim of this work is to investigate the above properties of mapping sequences. It is shown that the sufficient and necessary conditions which guarantee the periods and the linear spans of mapping sequences reach the maximum values. The special kind of bases of GF(q m) over GF(q) found is one in which the autocorrelation functions of such mapping sequences are 3-valued. We point out that mapping sequences are of considerable theoretical importance. The result of autocorrelation functions can be used to solve the minimum distance of one kind of burst error correcting codes. The practical importance relies on the fact that the set of generalized mapping sequences contains a lot of well-known sequences (i. e., multiplexed sequences, clock controlled sequences, GMW sequences or generalized GMW seqences and No sequences).
Work carried out in the framework of the agreement between the Italian PT Administration and the Fondazione “Ugo Bordoni”.
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© 1993 Springer-Verlag Berlin Heidelberg
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Gong, G. (1993). A new class of sequences: Mapping sequences. In: Cohen, G., Mora, T., Moreno, O. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1993. Lecture Notes in Computer Science, vol 673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56686-4_40
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DOI: https://doi.org/10.1007/3-540-56686-4_40
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