134 research outputs found
Improved asymptotic bounds for codes using distinguished divisors of global function fields
For a prime power , let be the standard function in the
asymptotic theory of codes, that is, is the largest
asymptotic information rate that can be achieved for a given asymptotic
relative minimum distance of -ary codes. In recent years the
Tsfasman-Vl\u{a}du\c{t}-Zink lower bound on was improved by
Elkies, Xing, and Niederreiter and \"Ozbudak. In this paper we show further
improvements on these bounds by using distinguished divisors of global function
fields. We also show improved lower bounds on the corresponding function
for linear codes
Error linear complexity measures for multisequences
Complexity measures for sequences over finite fields, such as the linear complexity and the k-error linear complexity, play an important role in cryptology. Recent developments in stream ciphers point towards an interest in word-based stream ciphers, which require the study of the complexity of multisequences. We introduce various options for error linear complexity measures for multisequences. For finite multisequences as well as for periodic multisequences with prime period, we present formulas for the number of multisequences with given error linear complexity for several cases, and we present lower bounds for the expected error linear complexity
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