与分组码相关的代数的块对角化
Block diagonalization for algebra's associated with block codes
摘要：
对于矩阵 *-代数B，考虑由B的n重张量积中的对称张量组成的矩阵 *-代数A。在编码理论中，这种代数的例子包括（非）二元汉明立方体的Bose-Mesner代数和Terwilliger代数，以及使用矩矩阵编码边界的SDP-层次中产生的代数。我们给出了一个计算效率块对角化的A在给定的块对角化的B，并制定了一些例子，包括Terwilliger代数的二进制和非二进制汉明立方体。作为一种工具，我们使用一些关于对称群表示的基本事实。
英文摘要：
For a matrix *-algebra B, consider the matrix *-algebra A consisting of the symmetric tensors in the n-fold tensor product of B. Examples of such algebras in coding theory include the Bose-Mesner algebra and Terwilliger algebra of the (non)binary Hamming cube, and algebras arising in SDP-hierarchies for coding bounds using moment matrices. We give a computationally efficient block diagonalization of A in terms of a given block diagonalization of B, and work out some examples, including the Terwilliger algebra of the binary- and nonbinary Hamming cube. As a tool we use some basic facts about representations of the symmetric group.
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