Codes of constant Lee or Euclidean weightJay

Carlet 2] has determined the linear codes over Z=(4) of constant Lee weight. This extended abstract describes a diierent approach to this problem, along the lines of 4], which has the potential to apply to a wide class of examples. In particular, we show that linear codes of constant Lee or Euclidean weight seldom exist over Z=(p 2) when p is an odd prime. Over nite elds, any linear code with constant Hamming weight is a replication of simplex (i.e., dual Hamming) codes. There are several proofs of this result, including 1], 3], and 4]. Recently, Carlet 2] has proved a similar result for linear codes of constant Lee weight over Z=(4), indeed, over any Z=(2 m). In this extended abstract we generalize the approach of 4]. While more complicated than Carlet's proof, our approach has the potential to apply to a wide class of weight functions over any nite commutative chain ring. For the purposes of this extended abstract, we will discuss codes over rings of the form Z=(p 2), p prime. In the case of Z=(4), we recover Carlet's result as Theorem 6. For p odd, we show in Theorem 11 that very few constant weight codes exist.