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This is a pictorial representation of a code concatenation, and, in particular, the Reed–Solomon code with n=q=4 and k=2 is used as the outer code and the Hadamard code with n=q and k=log q is used as the inner code. Overall, the concatenated code is a [, ]-code.
Pandas is built around data structures called Series and DataFrames. Data for these collections can be imported from various file formats such as comma-separated values, JSON, Parquet, SQL database tables or queries, and Microsoft Excel. [8] A Series is a 1-dimensional data structure built on top of NumPy's array.
The strings over an alphabet, with the concatenation operation, form an associative algebraic structure with identity element the null string—a free monoid. Sets of strings with concatenation and alternation form a semiring, with concatenation (*) distributing over alternation (+); 0 is the empty set and 1 the set consisting of just the null ...
The concatenation of the three strings "hello", " ", "world" can be computed by concatenating the first two strings (giving "hello ") and appending the third string ("world"), or by joining the second and third string (giving " world") and concatenating the first string ("hello") with the result. The two methods produce the same result; string ...
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The row-polymorphic record type defines a list of fields with their corresponding types, a list of missing fields, and a variable indicating the absence or presence of arbitrary additional fields.
The vectorization is frequently used together with the Kronecker product to express matrix multiplication as a linear transformation on matrices. In particular, = for matrices A, B, and C of dimensions k×l, l×m, and m×n.
Besides the usual set operations like union, intersection etc., concatenation can be applied to languages: if both and are languages, their concatenation is defined as the set of concatenations of any string from and any string from , formally = {}.