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

Jong-Seon No, Dong-Joon Shin, Tor Helleseth
2004 Designs, Codes and Cryptography  
In this paper, 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.  ... 
doi:10.1023/b:desi.0000032604.18844.31 fatcat:dttskc6sqndexeahtddbo527ay

On the p-ranks and characteristic polynomials of cyclic difference sets

Jong-Seon No, Dong-Joon Shin, T. Helleseth
Proceedings IEEE International Symposium on Information Theory,  
In this paper, 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.  ... 
doi:10.1109/isit.2002.1023368 fatcat:djfedpnuqbbjfk5y3hv77trnvy

Cyclicity and controlability in linear time-invariant systems

P. Antsaklis
1978 IEEE Transactions on Automatic Control  
New tests 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.  ... 
doi:10.1109/tac.1978.1101807 fatcat:oidrkcuptfd43fvfzpq44vd5dy

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]

Hikmet Yildiz, Netanel Raviv, Babak Hassibi
2020 arXiv   pre-print
Gabidulin codes over fields 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  ... 
arXiv:2004.14430v1 fatcat:u7c5sy5vdjf2zdoonodtbuvcda

A Complete Characterization of Irreducible Cyclic Orbit Codes [article]

Anna-Lena Trautmann, Joachim Rosenthal
2011 arXiv   pre-print
We derive some 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.  ... 
arXiv:1102.3167v4 fatcat:qaa5eskrp5fdlkb4vennbmmgsa

Sur la Structure de A-module de Drinfeld de rang 2 [article]

Mohamed Saadbouh Mohamed Ahmed
2006 arXiv   pre-print
Let P_Φ(X)= X^2-cX+μ 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.  ... 
arXiv:math/0606417v1 fatcat:e64zou473vftzg6hfqw2bbubp4

On Mordell-Weil group of isotrivial abelian varieties over function fields [article]

A. Libgober
2013 arXiv   pre-print
We show that 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).  ... 
arXiv:1209.4106v2 fatcat:jwharnlpzvanxog6tz4bzl34iy

The free m-cone of a matroid and its 𝒢-invariant [article]

Joseph E. Bonin, Kevin Long
2022 arXiv   pre-print
We prove analogous results for several variants 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.  ... 
arXiv:2106.00046v2 fatcat:jbxmsmh6dzgy3mvruz25lrvcxu

The A-module Structure Induced by a Drinfeld A-module over a Finite Field [article]

Mohamed Ahmed Mohamed saadbouh
2005 arXiv   pre-print
[T]/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  ... 
arXiv:math/0412368v5 fatcat:vpqzmgyffbeetkggs6fpzd4ecy

Integral representations of cyclic groups acting on relative holomorphic differentials of deformations of curves with automorphisms [article]

Sotiris Karanikolopoulos, Aristides Kontogeorgis
2012 arXiv   pre-print
We study integral representations 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.  ... 
arXiv:1203.0768v1 fatcat:7pxuog5e7fhaff4wswfwyza33q

Weight distribution of cyclic codes defined by quadratic forms and related curves

Ricardo A. Podestá, Denis E. Videla
2021 Revista de la Unión Matemática Argentina  
We describe 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.  ... 
doi:10.33044/revuma.1840 fatcat:uh45umoscjhl7c2ichmtzxofku

Integral representations of cyclic groups acting on relative holomorphic differentials of deformations of curves with automorphisms

Sotiris Karanikolopoulos, Aristides Kontogeorgis
2014 Proceedings of the American Mathematical Society  
We study integral representations 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.  ... 
doi:10.1090/s0002-9939-2014-12010-7 fatcat:32htpfhs4bbhfnuhtlc3pmpsuy

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

Dillon Mayhew
2008 SIAM Journal on Discrete Mathematics  
We define an order 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.  ... 
doi:10.1137/050640576 fatcat:p7izejhcovfyzp3jv6xh7dpjgq
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