2 results about "Dual code" patented technology

In coding theory, the dual code of a linear code C⊂𝔽qⁿ is the linear code defined by C⊥={x∈𝔽qⁿ∣〈x,c〉=0 ∀c∈C} where 〈x,c〉=∑ᵢ₌₁ⁿxᵢcᵢ is a scalar product. In linear algebra terms, the dual code is the annihilator of C with respect to the bilinear form <,>. The dimension of C and its dual always add up to the length n: dimC+dimC⊥=n. A generator matrix for the dual code is a parity-check matrix for the original code and vice versa.