Abstract
We introduce codes over an infinite family of rings and describe two Gray maps to binary codes which are shown to be equivalent. The Lee weights for the elements of these rings are described and related to the Hamming weights of their binary image. We describe automorphisms in the binary image corresponding to multiplication by units in the ring and describe the ideals in the ring, using them to define a type for linear codes. Finally, Reed Muller codes are shown as the image of linear codes over these rings.
Original language | English (US) |
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Pages (from-to) | 205-219 |
Number of pages | 15 |
Journal | Finite Fields and Their Applications |
Volume | 17 |
Issue number | 3 |
DOIs | |
State | Published - May 2011 |
Externally published | Yes |
Keywords
- Automorphisms
- Binary image
- Codes over rings
- Gray map
- Optimal codes
ASJC Scopus subject areas
- Theoretical Computer Science
- Algebra and Number Theory
- General Engineering
- Applied Mathematics