Geodesic
Modular adjacency algebras of Hamming schemes
Journal of Algebraic Combinatorics, Tome 20 (2004) no. 3, pp. 331-340.

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Summary: To each association scheme $G$ and to each field $R$, there is associated naturally an associative algebra, the so-called adjacency algebra $RG$ of $G$ over $R$. It is well-known that $RG$ is semisimple if $R$ has characteristic 0. However, little is known if $R$ has positive characteristic. In the present paper, we focus on this case. We describe the algebra $RG$ if $G$ is a Hamming scheme (and $R$ a field of positive characteristic). In particular, we show that, in this case, $RG$ is a factor algebra of a polynomial ring by a monomial ideal.
Keywords: association scheme, Hamming scheme, modular adjacency algebra 
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     author = {Yoshikawa, Masayoshi},
     title = {Modular adjacency algebras of {Hamming} schemes},
     journal = {Journal of Algebraic Combinatorics},
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     number = {3},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2004__20_3_a3/}
}
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Yoshikawa, Masayoshi. Modular adjacency algebras of Hamming schemes. Journal of Algebraic Combinatorics, Tome 20 (2004) no. 3, pp. 331-340. http://geodesic.mathdoc.fr/item/JAC_2004__20_3_a3/