Modular and p-adic cyclic codes
Designs, Codes and Cryptography
Cyclic codes over Z4, locator polynomials, and Newton's identities
IEEE Transactions on Information Theory
Affine Invariant and Cyclic Codes over p-adic Numbers and Finite Rings
Designs, Codes and Cryptography
Computational Discrete Mathematics
On the construction of skew quasi-cyclic codes
IEEE Transactions on Information Theory
Homogeneous weights and exponential sums
Finite Fields and Their Applications
New ring-linear codes from dualization in projective Hjelmslev geometries
Designs, Codes and Cryptography
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Certain nonlinear binary codes contain more codewords than any comparable linear code presentlyknown. These include the Kerdock and Preparata codes, which exist for all lengths 4^m ≥ 16. At length 16 theycoincide to give the Nordstrom-Robinson code. This paper constructs a nonlinear (64, 2^37, 12) code as the binaryimage, under the Gray map, of an extended cyclic code defined over the integers modulo 4 using Galois rings.The Nordstrom-Robinson code is defined in this same way, and like the Nordstrom-Robinson code, the new codeis better than any linear code that is presently known.