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Clear filtersLinearCode.dist_eq_minWtCodewords
Plain-language statement
The min distance of a linear code equals the minimum of the weights of non-zero codewords.
Source project: ArkLib
Person-level attribution pending.
LinearCode.eq_span_rows
Plain-language statement
A linear code is equal to the submodule spanned by the rows of the matrix whose rows form a basis of the code.
Source project: ArkLib
Person-level attribution pending.
LinearCode.gen_matrix_exists
Plain-language statement
Given a linear code of length ι and dimension dim over a field F, there exists a dim × ι matrix over F which generates the code. Theorem 2.2.7 [GRS25].
Source project: ArkLib
Person-level attribution pending.
LinearCode.projectedCode_linearCombination
Plain-language statement
Let T be a finite subset of ι. If every word in a collection lies in the projected code C|[T], then so do all F-linear combinations of these.
Source project: ArkLib
Person-level attribution pending.
LinearCode.singleton_bound_linear
Plain-language statement
Singleton bound for linear codes
Source project: ArkLib
Person-level attribution pending.
singleton_bound
Plain-language statement
Singleton bound for arbitrary codes
Source project: ArkLib
Person-level attribution pending.