1. Linear codes over 𝔽4R and their MacWilliams identity.
- Author
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Benbelkacem, Nasreddine, Ezerman, Martianus Frederic, and Abualrub, Taher
- Subjects
- *
LINEAR codes , *TWO-dimensional bar codes , *CODE generators , *GENERATORS of groups , *COMMUTATIVE rings - Abstract
Let 𝔽 4 be the field of four elements. We denote by R the commutative ring, with 1 6 elements, 𝔽 4 + v 𝔽 4 : = { a + v b | a , b ∈ 𝔽 4 } with v 2 = v. This work defines linear codes over the ring of mixed alphabets 𝔽 4 R as well as their dual codes under a nondegenerate inner product. We then derive the systematic form of the respective generator matrices of the codes and their dual codes. We wrap the paper up by proving the MacWilliams identity for linear codes over 𝔽 4 R. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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