A linear construction for certain Kerdock and Preparata codes
英文摘要：
The Nordstrom-Robinson, Kerdock, and (slightly modified) Pre\- parata codes are shown to be linear over $\ZZ_4$, the integers $\bmod~4$. The Kerdock and Preparata codes are duals over $\ZZ_4$, and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over $\ZZ_4$. This provides a simple definition for these codes and explains why their Hamming weight distributions are dual to each other. First- and second-order Reed-Muller codes are also linear codes over $\ZZ_4$, but Hamming codes in general are not, nor is the Golay code.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
