1. Introduction. In the problem of bounding the size of codes in compact homogeneous spaces, Del-sarte's polynomial method gives rise to the most powerful universal bounds on codes. Many overviews of the method exist in the literature; see for instance Levenshtein (1998). The purpose of this talk is to present a functional perspective of this method and give some examples. Let X be a compact me...

The Gilbert type bound for codes in the title is reviewed, both for small and large alphabets. Constructive lower bounds better than these existential bounds are derived from geometric codes, either over Fp or Fp2 , or over even degree extensions of Fp. In the latter case the approach is concatenation with a good code for the Hamming metric as outer code and a short code for the Lee metric as a...