Quantum Codes Constructed From Repeated-Root Cyclic Codes
نویسندگان
چکیده
منابع مشابه
Repeated-root cyclic codes
In the theory of cyclic codes, it is common practice to require that (n,q)= 1, where n is the word length and Fq is the alphabet. This ensures that the generator g ( x ) of the cyclic code has no multiple zeros ( = repeated mots). Furthermore it makes it possible to use an idempotent element as generator. However, much of the theory also goes through without the restriction on n and q. Recently...
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A parity-check matrix for a q -ary repeated-root cyclic code is derived using the Hasse derivative. Then the min imum distance of a q-ary repeated-root cyclic code C is expressecin terms of the min imum distance of a certain simple-root cyclic code C that is determined by C. With the help of this result, several binary repeated-root cyclic codes of lengths up to n = 62 are shown to contain the ...
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In papers by Castagnoli et al. and Van Lint, cyclic codeswith repeated roots are analyzed. Both papers fail to acknowledge apreviouswork by Chen, dating back to 1969, which includes an analysisof even, length binary cyclic codes. Results from Chen’s study arepresented. Index Terms -Binary cyclic codes of even length. In [l] and [2], the so called repeated-root cyclic codes h...
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We considered repeated-root cyclic codes whose block length is divisible by the characteristic of the underlying field. Cyclic self dual codes are also the repeated root cyclic codes. It is known about the one-level squaring construction for binary repeated root cyclic codes. In this correspondence, we introduced of two level squaring construction for binary repeated root cyclic codes of length...
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In this note, we present a construction of new nonbinary quantum codes with good parameters. These codes are obtained by applying the Calderbank-Shor-Steane (CSS) construction. In order to do this, we show the existence of (classical) cyclic codes whose defining set consists of only one cyclotomic coset containing at least two consecutive integers.
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ژورنال
عنوان ژورنال: Journal of Physics: Conference Series
سال: 2018
ISSN: 1742-6588,1742-6596
DOI: 10.1088/1742-6596/1069/1/012078