Primitive polynomials with a prescribed coefficient

Keywords

Mathematics, Degree (music), Polynomial, Conjecture, Finite field

References

• The three fixed coefficient primitive polynomial theoremStephen D. Cohen, Christopher King — 2004
• Existence of primitive polynomials with three coefficients prescribedDonald Mills — 2003
• p-adic Numbers, p-adic Analysis, and Zeta-FunctionsNeal Koblitz — 1977
• p-Adic formal series and primitive polynomials over finite fieldsShuqin Fan, Wenbao Han — 2004
• Primitive free cubics with specified norm and traceSophie Huczynska, Stephen D. Cohen — 2003
• Character Sums overp-adic FieldsWen-Ching Winnie Li — 1999
• Primitive polynomials over finite fieldsTom Hansen, Gary L. Mullen — 1992
• Primitive free quartics with specified norm and traceStephen D. Cohen, Sophie Huczynska — 2003
• The coefficients of primitive polynomials over finite fieldsWen Bao Han — 1996
• Distribution of irreducible polynomials of small degrees over finite fieldsKie Ham, Gary L. Mullen — 1998
• Primitive polynomials with first and second coefficients prescribedStephen D. Cohen, Donald Mills — 2003
• Primitive polynomial with three coefficients prescribedShuqin Fan, Wenbao Han — 2004
• Generators and irreducible polynomials over finite fieldsDaqing Wan — 1997
• Primitive elements and polynomials with arbitrary traceStephen D. Cohen — 1990
• p-adic Numbers, p-adic Analysis, and Zeta-FunctionsNeal Koblitz — 1984
• Primitive Polynomials over Small FieldsS. Cohen — 2003
• Open problems and conjectures in finite fieldsG. Mullen, I. Shparlinski — 1996

Cited by

• Existence Problems of Primitive Polynomials over Finite FieldsMateja Prešern — 2008
• Self-reciprocal irreducible polynomials with prescribed coefficientsTheodoulos Garefalakis — 2011
• Irreducible polynomials with consecutive zero coefficientsTheodoulos Garefalakis — 2008
• Explicit theorems on generator polynomialsStephen D. Cohen — 2005
• A generalization of the Hansen-Mullen conjecture on irreducible polynomials over finite fieldsDaniel Panario, Georgios Tzanakis — 2012
• PRIMITIVE POLYNOMIALS WITH PRESCRIBED SECOND COEFFICIENTStephen D. Cohen, Mateja Prešern — 2006
• Primitive normal polynomials with a prescribed coefficientShuqin Fan, Xiaozhe Wang — 2009
• On coefficients of polynomials over finite fieldsAmela Muratović-Ribić, Qiang Wang — 2011
• On the Existence of Some Specific Primitive Elements over Finite Fields of Even CharacteristicZhang Xiao, Peipei Wang, Xiwang Cao — 2012
• On certain diagonal equations over finite fieldsXiang‐dong Hou, Christopher Sze — 2009
• Primitive elements with prescribed traceXiwang Cao, Peipei Wang — 2014
• On the existence of some specific elements in finite fields of characteristic 2Peipei Wang, Xiwang Cao, Rongquan Feng — 2012
• On the Existence of Irreducible Polynomials with Prescribed Coefficients over Finite FieldsGeorgios Tzanakis — 2010
• Irreducible polynomials with prescribed sums of coefficientsAleksandr Tuxanidy, Qiang Wang — 2016
• On Asymptotic Behavior of the Ratio Between the Numbers of Binary Primitive and Irreducible PolynomialsYuri Borissov, Moon Ho Lee, Svetla Nikova⋆ — 2008
• Contributions aux opérateurs arithmétiques GF(2^m) et leurs applications à la cryptographie sur courbes elliptiques. (Contributions to GF(2^m) arithmetic operators for elliptic curve cryptography)Jérémy Métairie — 2016
• Prescribing coefficients of invariant irreducible polynomialsGiorgos Kapetanakis — 2017
• Characteristic digit-sum sequencesAleksandr Tuxanidy, Qiang Wang — 2018
• Certain Diagonal Equations over Finite FieldsChristopher Sze — 2009
• Problems on Permutation and Irreducible Polynomials Over Finite FieldsAleksandr Tuxanidy Torres — 2018

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