Abstract
The complete weight enumerator of the Delsarte–Goethals code over Z 4 is derived and an Assmus–Mattson-type approach at identifying t-designs in linear codes over Z 4 is presented. The Assmus–Mattson-type approach, in conjunction with the complete weight enumerator are together used to show that the codewords of constant Hamming weight in both the Goethals code over Z 4 as well as the Delsarte–Goethals code over Z 4 yield 3-designs, possibly with repeated blocks.
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Shin, DJ., Kumar, P.V. & Helleseth, T. An Assmus–Mattson-Type Approach for Identifying 3-Designs from Linear Codes over Z 4 . Designs, Codes and Cryptography 31, 75–92 (2004). https://doi.org/10.1023/A:1027338603957
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DOI: https://doi.org/10.1023/A:1027338603957