Browsing by Author "Shaska T"

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Codes over rings of size p2 and lattices over imaginary quadratic fields
(Finite Fields Appl., 2010) Shaska T; Shore C; Wijesiri G S
Let ?>0 be a square-free integer congruent to 3 mod 4 and OK the ring of integers of the imaginary quadratic field View the MathML source. Codes C over rings OK/pOK determine lattices ??(C) over K . If p?? then the ring R:=OK/pOK is isomorphic to Fp2 or Fp?Fp. Given a code C over R, theta functions on the corresponding lattices are defined. These theta series ???(C)(q) can be written in terms of the complete weight enumerators of C . We show that for any two ?
Degree 4 coverings of elliptic curves by genus 2
(Albanian J. Math., 2008) Shaska T; Wijesiri G S; Wolf S; Woodland L
Genus two curves covering elliptic curves have been the object of study of many articles. For a ?xed degree n the subloci of the moduli space M_2 of curves having a degree n elliptic subcover has been computed for n=3,5 and discussed in detail for n odd; see [17, 22, 3, 4]. When the degree of the cover is even the case in general has been treated in [16]. In this paper we compute the sublocus of M_2 of curves having a degree 4 elliptic subcover.
Theta nulls of cyclic curves of small genus
(Albanian J. Math., 2007) Previato E; Shaska T; Wijesiri G S
We study relations among the classical thetanulls of cyclic curves, namely curves X (of genus g(X)>1) with an automorphism ? such that ? generates a normal subgroup of the group G of automorphisms, and g(X???? )=0 .0. Relations between thetanulls and branch points of the projection are the object of much classical work, especially for hyperelliptic curves, and of recent work, in the cyclic case. We determine the curves of genus 2 and 3 in the locus Mg(G,C) for all G that have a normal subgroup ??? as above, and all possible signatures C, via relations among their thetanulls.