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Group code structures of affine-invariant codes. (English)
J. Algebra 325, No. 1, 269-281 (2011).
Let $GF(p^r)$ and $K=GF(p^m)$. Let $C$ be a group subalgebra of $F[K]$ identified with a linear code over $F$, $C\subset F^n$, where $n=p^m$. We say $C$ is even-like if, for each $(c_1,\dots,c_n)\in C$ $c_1+\dots +c_n=0$. We call $C$ a $p^r$-ary affine-invariant code if it is even-like and if the permutation automorphism group of $C$ (identified with the symmetric group on $K$) contains all the affine maps of $K$ (i.e., $x\mapsto ax+b$, $a\in K^\times$, $b\in K$). Among other things, the authors characterize those affine invariant codes which are group codes with respect to some non-abelian group. A well-written and interesting paper.
Reviewer: David Joyner (Annapolis)