In this note, we investigate the -norms of Barker polynomials and, more generally, Littlewood polynomials over the unit circle, and give improvements to some existing results.
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Gang Yu 1
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@article{CRMATH_2023__361_G3_609_0, author = {Gang Yu}, title = {A {Note} on {Barker} {Sequences} and the $L_1$-norm of {Littlewood} {Polynomials}}, journal = {Comptes Rendus. Math\'ematique}, pages = {609--616}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.428}, language = {en}, }
Gang Yu. A Note on Barker Sequences and the $L_1$-norm of Littlewood Polynomials. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 609-616. doi : 10.5802/crmath.428. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.428/
[1] Flat Littlewood polynomials exist, Ann. Math., Volume 192 (2020) no. 3, pp. 977-1004 | MR | Zbl
[2] Group synchronizing of binary digital systems, Communication Theory, Butterworths Sci. Pub., 1953, pp. 273-287
[3] Barker sequences and flat polynomials, Number theory and polynomials (London Mathematical Society Lecture Note Series), Volume 352, Cambridge University Press, 2008, pp. 71-88 | MR | Zbl
[4] Wieferich pairs and Barker sequences II, LMS J. Comput. Math., Volume 17 (2014), pp. 24-32 | DOI | MR | Zbl
[5] Sur un problème de Newman, C. R. Acad. Sci. Paris, Volume 324 (1997) no. 7, pp. 765-769 | DOI | MR | Zbl
[6] A note on the nonexistence of Barker sequences, Des. Codes Cryptography, Volume 2 (1992) no. 1, pp. 93-97 | DOI | MR | Zbl
[7] On a polynomial of Byrnes, Bull. Lond. Math. Soc., Volume 12 (1980) no. 3, pp. 219-224 | DOI | MR | Zbl
[8] The field descent method, Des. Codes Cryptography, Volume 36 (2005) no. 2, pp. 171-188 | DOI | MR | Zbl
[9] The anti-field-descent method, J. Comb. Theory, Ser. A, Volume 139 (2016), pp. 87-131 | DOI | MR | Zbl
[10] Wieferich pairs and Barker sequences, Des. Codes Cryptography, Volume 53 (2009) no. 3, pp. 149-163 | DOI | MR | Zbl
[11] Norms of polynomials, Am. Math. Mon., Volume 67 (1960), pp. 778-779 | DOI | MR | Zbl
[12] Barker sequences and Littlewood’s “two-sided conjectures” on polynomials with coefficients, Séminaire d’analyse harmonique. Année 1989/90., Université de Paris-Sud, Mathématiques, 1989, pp. 139-151
[13] Cyclotomic integers and finite geometry, J. Am. Math. Soc., Volume 12 (1999) no. 4, pp. 929-952 | DOI | MR | Zbl
[14] Barker sequences of odd length, Des. Codes Cryptography, Volume 80 (2016) no. 2, pp. 409-414 | DOI | MR | Zbl
[15] On Barker codes of even length, IEEE Trans. Inf. Theory, Volume 51 (1963) no. 9, p. 1256
[16] On the binary sequences, Proc. Am. Math. Soc., Volume 12 (1961), pp. 396-399 | MR | Zbl
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