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Download QR code; Print/export Download as PDF; Printable version; In other projects ... [1] [2] [3] Linear algebra is central to almost all areas of mathematics.
Chapter 5 studies cyclic codes and Chapter 6 studies a special case of cyclic codes, the quadratic residue codes. Chapter 7 returns to BCH codes. [1] [6] After these discussions of specific codes, the next chapter concerns enumerator polynomials, including the MacWilliams identities, Pless's own power moment identities, and the Gleason ...
The codewords in a linear block code are blocks of symbols that are encoded using more symbols than the original value to be sent. [2] A linear code of length n transmits blocks containing n symbols. For example, the [7,4,3] Hamming code is a linear binary code which represents 4-bit messages using 7-bit codewords. Two distinct codewords differ ...
[7] linear form A linear map from a vector space to its field of scalars [8] linear independence Property of being not linearly dependent. [9] linear map A function between vector space s which respects addition and scalar multiplication. linear transformation A linear map whose domain and codomain are equal; it is generally supposed to be ...
This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices. Linear equations
The Hamming(7,4) code is closely related to the E 7 lattice and, in fact, can be used to construct it, or more precisely, its dual lattice E 7 ∗ (a similar construction for E 7 uses the dual code [7,3,4] 2).
1.3 Linear algebra. 1.4 Group theory. 1.5 Polynomials. 1.6 Ring theory and commutative algebra. 1.7 Universal algebra. 2 Analysis. ... Download QR code; Print/export
aaa is a one- to three-letter code describing the actual algorithm implemented in the subroutine, e.g. SV denotes a subroutine to solve linear system, while R denotes a rank-1 update. For example, the subroutine to solve a linear system with a general (non-structured) matrix using real double-precision arithmetic is called DGESV . [ 2 ] : "