1,720,986 research outputs found
On maximum additive Hermitian rank-metric codes
No full textInspired by the work of Zhou (Des Codes Cryptogr 88:841–850, 2020) based on the paper of Schmidt (J Algebraic Combin 42(2):635–670, 2015), we investigate the equivalence issue of maximum d-codes of Hermitian matrices. More precisely, in the space Hn(q2) of Hermitian matrices over Fq2 we have two possible equivalences: the classical one coming from the maps that preserve the rank in Fq2n×n, and the one that comes from restricting to those maps preserving both the rank and the space Hn(q2). We prove that when d< n and the codes considered are maximum additive d-codes and (n- d) -designs, these two equivalence relations coincide. As a consequence, we get that the idealisers of such codes are not distinguishers, unlike what usually happens for rank metric codes. Finally, we deal with the combinatorial properties of known maximum Hermitian codes and, by means of this investigation, we present a new family of maximum Hermitian 2-code, extending the construction presented by Longobardi et al. (Discrete Math 343(7):111871, 2020)
On the List Decodability of Rank Metric Codes
No full textLet k,n,m in {mathbb Z} ^{+} be integers such that kleq n leq m , let mathrm {G}_{n,k}in {mathbb F} _{q^{m}}^{n} be a Delsarte-Gabidulin code. Recently, Wachter-Zeh proved that codes belonging to this family cannot be efficiently list decoded for any radius au , providing au is large enough. This achievement essentially relies on proving a lower bound for the list size of some specific words in {mathbb F}_{q^{m}}^{n}. Some years later, Raviv and Wachter-Zeh improved this bound in a special case, i.e. when nmid m. As a consequence, they were able to detect infinite families of Delsarte-Gabidulin codes that cannot be efficiently list decoded at all. In this article we determine similar lower bounds for Maximum Rank Distance codes belonging to a wider class of examples, containing Generalized Gabidulin codes, Generalized Twisted Gabidulin codes, and examples recently described by Trombetti and Zhou. By exploiting arguments such as those used by Raviv and Wachter-Zeh, when nmid m , we also show infinite families of generalized Gabidulin codes that cannot be list decoded efficiently at any radius greater than or equal to left lfloor{ rac {d-1}2 }
ight
floor +1 , where d is its minimum distance. Nonetheless, in all the examples belonging to above mentioned class, we detect infinite families that cannot be list decoded efficiently at any radius greater than or equal to left lfloor{ rac {d-1}2 }
ight
floor +2 , where d is its minimum distance. In particular, this leads to show infinite families of Gabidulin codes, with underlying parameters not already covered by the result of Raviv and Wachter-Zeh, having this decodability defect. Finally, relying on the properties of a set of subspace trinomials recently presented by McGuire and Mueller, we are able to prove our main result, that is any rank-metric code of {mathbb F}_{q^{m}}^{n} of order q^{kn} with n dividing m , such that 4n-3 is a square in mathbb {Z} and containing mathrm {G}_{n,2} , is not efficiently list decodable at some values of the radius au
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
On the sporadic semifield flock
No full textWe obtain the BLT-set associated with the sporadic semifield flock of the quadratic cone in
as the complete intersection of the Payne–Thas and the Kantor–Knuth ovoids of the
parabolic quadric . Also, we give an alternative construction of the Penttila–Williams ovoid of
Spreads in H(q) and 1-systems of Q(6,q)
No full textIn this paper we prove that the projections along reguli of a translation spread of the classical generalized hexagon H(q) are translation ovoids of Q(4,q). As translation ovoids of Q(4,2r) are elliptic quadrics, this forces that all translation spreads of H(2r) are semi-classical. By representing H(q) as a coset geometry, we obtain a characterization of a translation spread in terms of a set of points of PG(3,q) which belong to imaginary chords of a twisted cubic and we construct a new example of a semi-classical spread of H(2r). Finally, we study the semi-classical locally Hermitian 1-systems of Q(6,q) which are spreads of Q-(5,q)
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