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Note sur la notion d’équivalence entre deux codes linéaires. (French) Zbl 0632.94009

In this paper it is shown that the existence of a Hamming isometry sending a code C onto a code C’ implies the existence of a Hamming isometry sending C onto C’ whose restrictions to the simple components of C are semilinear. (A code is called simple if it is not the direct sum of two or more smaller codes having disjoint supports, the support of a code is the union of the supports of its elementary words (which are the words x in C such that there does not exist a word x’ in C with supp(x’) contained in supp(x)).)
In the case where C is a subspace of \({\mathbb{F}}^ n\), where \({\mathbb{F}}\) is of prime order, it has been proved that such a Hamming isometry is linear.
The paper is well written and I think the results are nice. However example (3) on page 181 is incorrect: The code \(C={\mathbb{F}}^ 2_ 2\) is cyclic but not simple since \(C=<(1\quad 0)>\oplus <(0\quad 1)>.\)
Reviewer: H.J.Tiersma

MSC:

94B05 Linear codes (general theory)
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
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References:

[1] Bonneau, P., Codes et Combinatoire, Thèse de 3eme Cycle (1984), Paris VI
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