Abstract | ||
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Let
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>
be a prime,
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$s$ </tex-math></inline-formula>
be a positive integer, and let
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$b$ </tex-math></inline-formula>
be an integer satisfying
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \leq b < p^{s}$ </tex-math></inline-formula>
. In this paper, we obtain
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$b$ </tex-math></inline-formula>
-symbol distances of all repeated-root constacyclic codes of length
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p^{s}$ </tex-math></inline-formula>
over finite fields. Using this result, we determine
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$b$ </tex-math></inline-formula>
-symbol distances of all repeated-root constacyclic codes of length
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p^{s}$ </tex-math></inline-formula>
over finite commutative chain rings. We also list all MDS
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$b$ </tex-math></inline-formula>
-symbol repeated-root constacyclic codes of length
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p^{s}$ </tex-math></inline-formula>
over finite fields, and all MDS
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$b$ </tex-math></inline-formula>
-symbol repeated-root constacyclic codes of length
<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p^{s}$ </tex-math></inline-formula>
over finite commutative chain rings in general. |
Year | DOI | Venue |
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2019 | 10.1109/TIT.2019.2937858 | IEEE Transactions on Information Theory |
Keywords | DocType | Volume |
Cyclic codes,negacyclic codes,local rings,optimal codes | Journal | 65 |
Issue | ISSN | Citations |
12 | 0018-9448 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
---|---|---|---|
Anuradha Sharma | 1 | 10 | 8.49 |
Tania Sidana | 2 | 0 | 1.01 |