Rank formulas for certain products of matrices

Ahlswede R, Cai N (1993)
Applicable Algebra in Engineering, Communication and Computing 4(4): 253-261.

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For two matrix operations, called quasi-direct sum and quasi-outer product, we determine their deviations from multiplicative behaviour of the rank. The second operation arises in the determination of the function table for so-called sum-type functions such as the Hamming distance. A consequence of the corresponding rank formula is, that the frequently used log rank can be a very poor bound for two-way communication complexity. Instead, as was shown in [9], a certainexponential rank gives often excellent or even optimal bounds.
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Ahlswede R, Cai N. Rank formulas for certain products of matrices. Applicable Algebra in Engineering, Communication and Computing. 1993;4(4):253-261.
Ahlswede, R., & Cai, N. (1993). Rank formulas for certain products of matrices. Applicable Algebra in Engineering, Communication and Computing, 4(4), 253-261.
Ahlswede, R., and Cai, N. (1993). Rank formulas for certain products of matrices. Applicable Algebra in Engineering, Communication and Computing 4, 253-261.
Ahlswede, R., & Cai, N., 1993. Rank formulas for certain products of matrices. Applicable Algebra in Engineering, Communication and Computing, 4(4), p 253-261.
R. Ahlswede and N. Cai, “Rank formulas for certain products of matrices”, Applicable Algebra in Engineering, Communication and Computing, vol. 4, 1993, pp. 253-261.
Ahlswede, R., Cai, N.: Rank formulas for certain products of matrices. Applicable Algebra in Engineering, Communication and Computing. 4, 253-261 (1993).
Ahlswede, Rudolf, and Cai, Ning. “Rank formulas for certain products of matrices”. Applicable Algebra in Engineering, Communication and Computing 4.4 (1993): 253-261.
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