Geodesic
Positive integer solutions of systems of linear equations and polynomials of small weight divisible by~$(1-x)^r$
Diskretnaya Matematika, Tome 26 (2014) no. 2, pp. 131-142.

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A. S. Rybakov. Positive integer solutions of systems of linear equations and polynomials of small weight divisible by~$(1-x)^r$. Diskretnaya Matematika, Tome 26 (2014) no. 2, pp. 131-142. http://geodesic.mathdoc.fr/item/DM_2014_26_2_a8/

[1] Kassels Dzh. V. S., Vvedenie v teoriyu diofantovykh priblizhenii, Izd. inostr. lit., Moskva, 1961, 213 pp. | MR

[2] Korn G., Korn T., Spravochnik po matematike, Nauka, Moskva, 1973, 831 pp.

[3] Sazonov D. M., Antenny i ustroistva SVCh, Vysshaya Shkola, Moskva, 1988, 434 pp.

[4] Skhreiver A., Teoriya lineinogo i tselochislennogo programmirovaniya, v. 1, 2, Mir, Moskva, 1991, 702 pp.

[5] Feldman N. I., Sedmaya problema Gilberta, Nauka, Moskva, 1982, 311 pp. | MR

[6] Borwein P., Erdélyi T., “On the zeros of polynomials with restricted coefficients”, Illinois J. Math., 41 (1997), 667–675 | MR | Zbl

[7] Boyd D. W., “On a problem of Byrnes concerning polynomials with restricted coefficients”, Math. Comput., 66:220 (1997), 1697–1703 | DOI | MR | Zbl

[8] Boyd D. W., “On a problem of Byrnes concerning polynomials with restricted coefficients, II”, Math. Comput., 71:239 (2001), 1205–1217 | DOI | MR

[9] Byrnes J. S., “Problems on polynomials with restricted coefficients arising from questions in antenna array theory”, Recent Advances in Fourier Analysis and Its Applications, eds. J. S. Byrnes, J. F. Byrnes, Kluwer Academic Publishers, Dordrecht, 1990, 677–678 | DOI

[10] Byrnes J. S., Newman D. J., “Null steering employing polynomials with restricted coefficients”, IEEE Trans. Antennas and Propagation, 36 (1988), 301–303 | DOI

[11] Lagarias J. C., Lenstra H. W., Schnorr C. P., Korkine–Zolotareff bases and successive minima of a lattice and its reciprocial lattice, Tech. Rept. MSRI 07718-86, Math. Sci. Res. Inst., Berkley, 1986, 122–146

[12] Mignotte M., “Sur les polynômes divisibles par $(X-1)^n$”, Arithmetix, 1980, no. 2, 28–29

[13] Prometheus Inc. Polynomials with restricted coefficients and their applications, Tech. rep. 88 0092, Air Force Office of Scientific Research, 1990

[14] Prometheus Inc. New approaches to beamforming, null steering and filtering, Tech. rep. 90 0866, Air Force Office of Scientific Research, 1988

[15] Schnorr C. P., “A hierarchy of polynomial time lattice basis reduction algorithms”, Theoretical Computer Science, 53 (1987), 201–224 | DOI | MR | Zbl

[16] Shoup V., NTL: A Library for doing Number Theory, , Dep. Comput. Sci., Wisconsin–Madison http://www.shoup.net/