Abstract
The concept of parity check matrices of linear binary codes has been extended by Heden [10] to parity check systems of nonlinear binary codes. In the present paper we extend this concept to parity check systems of nonlinear codes over finite commutative Frobenius rings. Using parity check systems, results on how to get some fundamental properties of the codes are given. Moreover, parity check systems and its connection to characters is investigated and a MacWilliams type theorem on the distance distribution is given.
Original language | English |
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Pages (from-to) | 409-427 |
Number of pages | 19 |
Journal | Advances in Mathematics of Communications |
Volume | 11 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2017 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Characters
- Discrete fourier analysis
- Finite commutative frobenius rings
- MacWilliams type theorem
- Nonlinear codes
- Parity check systems