An Assmus–Mattson theorem for codes over commutative association schemes

John Vincent S. Morales, Hajime Tanaka

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We prove an Assmus–Mattson-type theorem for block codes where the alphabet is the vertex set of a commutative association scheme (say, with s classes). This in particular generalizes the Assmus–Mattson-type theorems for Z4-linear codes due to Tanabe (Des Codes Cryptogr 30:169–185, 2003) and Shin et al. (Des Codes Cryptogr 31:75–92, 2004), as well as the original theorem by Assmus and Mattson (J Comb Theory 6:122–151, 1969). The weights of a code are s-tuples of non-negative integers in this case, and the conditions in our theorem for obtaining t-designs from the code involve concepts from polynomial interpolation in s variables. The Terwilliger algebra is the main tool to establish our results.

Original languageEnglish
Pages (from-to)1039-1062
Number of pages24
JournalDesigns, Codes, and Cryptography
Issue number5
Publication statusPublished - 2018 May 1


  • Assmus–Mattson theorem
  • Association scheme
  • Code
  • Design
  • Multivariable polynomial interpolation
  • Terwilliger algebra


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