1. A circuitry for a correction of errors in a possibly erroneous binary word v?=v?1, . . . , v?n relative to a codeword v=v1, . . . , vn, the circuitry comprising:

a syndrome generator for determining an error syndrome s=(s1, s3) according to a modified BCH code with a H-matrix Hmod comprising a first BCH submatrix H1mod and a second BCH submatrix H3mod, and with a code distance d?5,

wherein n? column vectors of the BCH submatrix H1mod are paired as column vector pairs so that a componentwise XOR combination of the two column vectors of each column vector

pair produces an identical column vector K that is different from all column vectors of the first BCH submatrix H1mod and where n? is even and 4?n??n applies,

wherein the second BCH submatrix H3mod comprises a corresponding column vector for each column vector in the first BCH submatrix H1mod so that the corresponding column vector is a third power, according to Galois field arithmetic, of the column vector in the

first BCH submatrix H1mod,

wherein the syndrome generator is configured to determine the error syndrome s by multiplying the H-matrix Hmod with the possibly erroneous binary word v? so that a first error syndrome portion is given by s1=H1mod·v? and a second error syndrome portion is given by s3=H3mod·v?; and

a decoder for generating a correction vector e=(e1, . . . , en) with correction values ej=ej+1=el=1 and et=0 for t?j, j+1, l, if the first error syndrome portion s1 equals the componentwise XOR combination of the identical column vector K and a column vector at a column position l of the

first BCH submatrix H1mod, and if the second error syndrome portion s3 equals the componentwise XOR combination of column vectors at column positions j, j+1, and l of the second BCH submatrix H3mod.