On primitive BCH codes with unequal error protection capabilities

where H i m ) = -mlog2 ( U ) (1 crjlog, (1 a). In this correspondence we present new estimates of the relative error term improving the known results. Our approach is based on investigating upper bounds for absolute values of Krawtchouk polynomials. Actually, this is just a refinement of an idea due to P. Sol6 [ 161. The bounds obtained are quite tight. Particularly, for t fixed our estimate is of order at most O ( i t ' ). This approach can be easily generalized to arbitrary codes with known dual distance width, see e.g., [3]. As it was mentioned by an anonymous referee, the approach works as well for wide classes of Goppa codes, Melas codes, etc., where bounds of Carlitz-Uchiyama type for the dual distance width are known (see, e.g. [ 5 ] ,161, [ I l l , [12]). Another upper estimates for values of Krawtchouk polynomials can be found in [4] where the expression for the envelope of absolute values of Krawtchouk polynomials was obtained.