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Given two quadratic lattices $M$ and $N$ over a dyadic local field $F$, i.e.a finite extension of ${\mathbb Q}$, we give necessary and sufficientconditions such that $M$ represents $N$. Previous results on this problem wereobtained by O.T. O'Meara in 1958, who solved this problem in the case when thebase field $F$ is 2-adic, i.e. a non-ramified extension of ${\mathbb Q}_2$, andby C. Riehm in 1964, who solved the case when $M$ is unimodular. Some notablework on quadratic forms over dyadic local fields, in particular, onrepresentations has also been done by Fei Xu.  Our result is given in terms of BONGs (bases of norm generators), which is anew way to describe quadratic lattices over dyadic local fields, complimentaryto the more traditional Jordan splittings. However, they can be easilytranslated in the language of Jordan splittings. The use of BONGs is not meantto completely replace the Jordan splitting. Neither they make the proofsshorter. The study of quadratic lattices over dyadic local fields is well knownto be very complicated and technical. However, by using BONGs the results canbe written in a more compact form and it is easier to make educated guesses ongeneral results by extrapolating results in small dimensions.

Representations of quadratic lattices over dyadic local fields