Skew cyclic codes over F4R

• Main Authors: Benbelkacem, Nasreddin, Ezerman, Martianus Frederic, Abualrub, Taher, Aydin, Nuh, Batoul, Aicha
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2021
• Subjects: Science::Mathematics; Linear Codes; Skew Cyclic Codes
• Online Access: https://hdl.handle.net/10356/146375
• Institution: Nanyang Technological University

This paper considers a new alphabet set, which is a ring that we call 4R, to construct linear error-control codes. Skew cyclic codes over this ring are then investigated in details. We define a nondegenerate inner product and provide a criteria to test for self-orthogonality. Results on the algebraic structures lead us to characterize 4R-skew cyclic codes. Interesting connections between the image of such codes under the Gray map to linear cyclic and skew-cyclic codes over 4 are shown. These allow us to learn about the relative dimension and distance profile of the resulting codes. Our setup provides a natural connection to DNA codes where additional biomolecular constraints must be incorporated into the design. We present a characterization of R-skew cyclic codes which are reversible complement.