Type-II polyadic constacyclic codes over finite fields
Polyadic constacyclic codes over finite fields have been of interest due to their nice algebraic structures, good parameters, and wide applications. Recently, the study of Type-I m-adic constacyclic codes over finite fields has been established. In this paper, a family of Type-II m-adic constacycli...
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| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/156043 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | Polyadic constacyclic codes over finite fields have been of interest due to their nice algebraic structures, good parameters, and wide applications. Recently, the study of Type-I
m-adic constacyclic codes over finite fields has been established. In this paper, a family of Type-II m-adic constacyclic codes is investigated. The existence of such codes is
determined using the length of orbits in a suitable group action. A necessary condition
and a sufficient condition for a positive integer s to be a multiplier of a Type-II m-adic
constacyclic code are determined. Subsequently, for a given positive integer m, a necessary condition and a sufficient condition for the existence of Type-II m-adic constacyclic
codes are derived. In many cases, these conditions become both necessary and sufficient.
For the other cases, determining necessary and sufficient conditions is equivalent to the
discrete logarithm problem which is considered to be computationally intractable. Some
special cases are investigated together with examples of Type-II polyadic constacyclic
codes with good parameters. |
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