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On the p-Ranks and Characteristic Polynomials of Cyclic Difference Sets

2004
*
Designs, Codes and Cryptography
*

In this paper,

doi:10.1023/b:desi.0000032604.18844.31
fatcat:dttskc6sqndexeahtddbo527ay
*the**p*-*ranks**and**characteristic**polynomials**of**cyclic**difference**sets*are derived by expanding*the*trace expressions*of*their*characteristic*sequences. ... Also,*the**p*-*rank**of*a Singer*difference**set*is reviewed*and**the**characteristic**polynomial*is calculated using our approach. ... Acknowledgments This work was supported in part by*the*Korean Ministry*of*Information*and*Communications*and**the*Norwegian Research Council. ...##
###
On the p-ranks and characteristic polynomials of cyclic difference sets

*
Proceedings IEEE International Symposium on Information Theory,
*

In this paper,

doi:10.1109/isit.2002.1023368
fatcat:djfedpnuqbbjfk5y3hv77trnvy
*the**p*-*ranks**and**characteristic**polynomials**of**cyclic**difference**sets*are derived by expanding*the*trace expressions*of*their*characteristic*sequences. ... Also,*the**p*-*rank**of*a Singer*difference**set*is reviewed*and**the**characteristic**polynomial*is calculated using our approach. ... Acknowledgments This work was supported in part by*the*Korean Ministry*of*Information*and*Communications*and**the*Norwegian Research Council. ...##
###
Cyclicity and controlability in linear time-invariant systems

1978
*
IEEE Transactions on Automatic Control
*

New tests

doi:10.1109/tac.1978.1101807
fatcat:oidrkcuptfd43fvfzpq44vd5dy
*of**cyclicity**and*contrdlability (observabiity), together with new algorithms to evaluate*the*controllable (-able) modes*and**the*minimal*polynomial*are also presented. ... Absrma-A number*of*results, involving*the*notions*of*contrdlability (observability)*and**cyclicity*in a h e a r time-invahnt control system, are derived using a new basic theorem. ...*The*following proof is completely*different**and*much simpler.)*P*I 1 n m TRANSACTIONS*ON*AUTOMATIC CONTROL, VOL. ...##
###
Page 3177 of Mathematical Reviews Vol. , Issue 2000e
[page]

2000
*
Mathematical Reviews
*

A symmetric group action

*on**the*maximal chains*of*a finite*ranked*poset was defined by R.*P*. ... I Math. 294 (1982), no. 13, 447-450; MR 83e:14039] with*the*Q-*polynomials**of**P*. Pragacz*and*J. ...##
###
Support Constrained Generator Matrices of Gabidulin Codes in Characteristic Zero
[article]

2020
*
arXiv
*
pre-print

Gabidulin codes over fields

arXiv:2004.14430v1
fatcat:u7c5sy5vdjf2zdoonodtbuvcda
*of**characteristic*zero were recently constructed by Augot et al., whenever*the*Galois group*of**the*underlying field extension is*cyclic*. ... In particular, a certain condition pertaining*the*intersection*of*zero entries at*different*rows, was shown to be necessary*and*sufficient for*the*existence*of**the*sparsest possible generator matrix*of*...*one*with a smaller parameter, whereas in*the**characteristic*zero,*the*entries are in*the*form*of*θ-*polynomials*(defined in [3] )*and*applying*the*same step turns*the*problem into*one**of*a*different*kind ...##
###
A Complete Characterization of Irreducible Cyclic Orbit Codes
[article]

2011
*
arXiv
*
pre-print

We derive some

arXiv:1102.3167v4
fatcat:qaa5eskrp5fdlkb4vennbmmgsa
*of**the*basic properties*of*these codes such as*the*cardinality*and**the*minimum distance. ... We give a complete list*of*orbit codes that are generated by an irreducible*cyclic*group, i.e. an irreducible group having*one*generator. ... Moreover,*polynomials**of**the*same degree*and*same order generate codes with*the*same cardinality*and*minimum distance. ...##
###
Sur la Structure de A-module de Drinfeld de rang 2
[article]

2006
*
arXiv
*
pre-print

Let P_Φ(X)= X^2-cX+μ

arXiv:math/0606417v1
fatcat:e64zou473vftzg6hfqw2bbubp4
*P*^m (c an element*of*F_q[T], μ be a non-vanishing element*of*m*the*degree*of**the*extension L over*the*field*and**P**the*F_q[T]-*characteristic**of**of**the**polynomial**P*)*the**characteristic*...*polynomial**of**the*Frobenius F*of*L. ... an ordinary Drinfeld A-module*of**rank*2,*and*let ρ an ideal from A*different*from*the*A-*characteristic**P**of*L, such that ρ 2 |*P*Φ (1)*and*ρ | c−2. ...##
###
On Mordell-Weil group of isotrivial abelian varieties over function fields
[article]

2013
*
arXiv
*
pre-print

We show that

arXiv:1209.4106v2
fatcat:jwharnlpzvanxog6tz4bzl34iy
*the*Mordell Weil*rank**of*an isotrivial abelian variety with a*cyclic*holonomy depends only*on**the*fundamental group*of**the*complement to*the*discriminant provided*the*discriminant has singularities ... As a corollary we give a family*of*simple Jacobians over field*of*rational functions in two variable for which*the*Mordell Weil*rank*is arbitrary large. ... (17) ∆*p*,q = (t pq − 1)(t − 1) (t*p*− 1)(t q − 1)*The**characteristic**polynomial**of**the*action*on*Gr 0 [32]*and*references there). ...##
###
The free m-cone of a matroid and its 𝒢-invariant
[article]

2022
*
arXiv
*
pre-print

We prove analogous results for several variants

arXiv:2106.00046v2
fatcat:jbxmsmh6dzgy3mvruz25lrvcxu
*of**the*free m-cone. We also define a new matroid invariant*of*M,*and*show that it determines*the*Tutte*polynomial**of*Q_m(M). ...*and*Q_m(N) have*the*same 𝒢-invariant but*different*configurations. ... ACKNOWLEDGMENTS We thank Joseph Kung for valuable observations*and*comments*on**the*topics*of*this paper. ...##
###
The A-module Structure Induced by a Drinfeld A-module over a Finite Field
[article]

2005
*
arXiv
*
pre-print

[T]/

arXiv:math/0412368v5
fatcat:vpqzmgyffbeetkggs6fpzd4ecy
*P*,*P*is a F d*the*degree*of**the**polynomial**P*)*the**characteristic**polynomial*,*of**the*Frobenius F*of*L. ... Let Φ be a Drinfeld F_q[T]-module*of**rank*2, over a finite field L, a finite extension*of*n degrees for a finite field with q elements element*of*F_q, m*the*degree*of**the*extension L over*the*field F_q ...*The**characteristic**polynomial**of*Frobenius endomorphism F is : Proposition 4 . 3 . 43 Let Φ be an ordinary Drinfeld A-module*of**rank*2,*and*let ρ an ideal from A*different*from*the*A-*characteristic**P*...##
###
Integral representations of cyclic groups acting on relative holomorphic differentials of deformations of curves with automorphisms
[article]

2012
*
arXiv
*
pre-print

We study integral representations

arXiv:1203.0768v1
fatcat:7pxuog5e7fhaff4wswfwyza33q
*of*holomorphic differentials*on**the*Oort-Sekiguci-Suwa component*of*deformations*of*curves with*cyclic*group actions. ...*The*matrix (a ij ) is lower triangular*and*in*characteristic**p**the*matrix A a has order*p*. Let G = σ be a*cyclic*group*of*order*p*. ... This is compatible also with*the*fact that*the*isomorphism type*of*a modular representation for*the**cyclic*group depends only*on**the**rank**of**the*module. Definition 5. ...##
###
Weight distribution of cyclic codes defined by quadratic forms and related curves

2021
*
Revista de la Unión Matemática Argentina
*

We describe

doi:10.33044/revuma.1840
fatcat:uh45umoscjhl7c2ichmtzxofku
*the*spectra for all these codes when L is an even*rank*family, in terms*of**the*distribution*of**ranks**of**the*forms Q R in*the*family L,*and*we also compute*the*complete weight enumerator for ... In particular, considering*the*family L = x q , with fixed in N, we give*the*weight distribution*of*four parametrized families*of**cyclic*codes C , C ,0 , C ,1 ,*and*C ,2 over Fq with zeros*and*m/(m, ) ...*The*family L = x*p*, x 3*of**p*-linearized*polynomials*over F*p*m has*the*even*rank*property, by Theorem 5.1. ...##
###
Integral representations of cyclic groups acting on relative holomorphic differentials of deformations of curves with automorphisms

2014
*
Proceedings of the American Mathematical Society
*

We study integral representations

doi:10.1090/s0002-9939-2014-12010-7
fatcat:32htpfhs4bbhfnuhtlc3pmpsuy
*of*holomorphic differentials*on**the*Oort-Sekiguchi-Suwa component*of*deformations*of*curves with*cyclic*group actions. ...*The*matrix (a ij ) is lower triangular,*and*in*characteristic**p**the*matrix A a has order*p*. Let G = σ be a*cyclic*group*of*order*p*. ... This is also compatible with*the*fact that*the*isomorphism type*of*a modular representation for*the**cyclic*group depends only*on**the**rank**of**the*module. Remark 5. ...##
###
Page 759 of Mathematical Reviews Vol. , Issue 2001B
[page]

2001
*
Mathematical Reviews
*

(NL-PRL; Eindhoven);
Krattenthaler, Christian (A-WIEN; Vienna);
Xiang, Qing (1-DE; Newark, DE)
Gauss sums, Jacobi sums,

*and**p*-*ranks**of**cyclic**difference**sets*. (English summary) J. Combin. Theory Ser. ... More- 2001b:05040 over, a generalized MCM*polynomial*for # = 0, | is (shal = + pTi(e)) -*P*(z) = First*of*all an explicit*one*-to-*one*correspondence between these two classes*of**polynomials*is given. ...##
###
Matroid Complexity and Nonsuccinct Descriptions

2008
*
SIAM Journal on Discrete Mathematics
*

We define an order

doi:10.1137/050640576
fatcat:p7izejhcovfyzp3jv6xh7dpjgq
*on**the*various methods*of*description,*and*we show how this order acts upon 10 types*of*input. ...*The*computational complexity*of*algorithmic problems under this scheme appears to be highly dependent*on**the*choice*of*input type. ... I also thank*the*referees for their constructive comments. In particular,*the*question*of**the*existence*of*FPT algorithms for DETECTING AN N -MINOR was raised by*one**of**the*referees. ...
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