In group theory and coding theory, a **coset leader** is a concept used to describe a representative (or "leader") from a set of cosets of a subgroup within a group. More specifically, it is often employed in the context of error-correcting codes. When dealing with linear codes, the idea of a coset leader becomes particularly important. A linear code can be viewed as a vector space over a finite field.
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A coset leader is a minimum-Hamming-weight word in a coset of a linear code. It represents a most economical error pattern with the associated syndrome. Several leaders can tie; they need not be unique outside the code's guaranteed correction radius.