Let p be a prime number. Reducible cyclic codes of rank 2 over $$\mathbb {Z}_{p^m}$$ are shown to have exactly two Hamming weights in some cases. Their weight distribution is computed explicitly. When these projective, the coset graphs their dual strongly regular. The spectra determined.

The symmetry algebra of asymptotically flat spacetimes at null infinity in three dimensions is the semi-direct sum of the infinitesimal diffeomorphisms on the circle with an abelian ideal of supertranslations. The associated charge algebra is shown to admit a non trivial classical central extension of Virasoro type closely related to that of the anti-de Sitter case. PACS numbers: 04.20.Ha, 04.6...

Designing a non-ideal delay line (DL) with phase distortion in a transmitted-reference ultra-wideband system (TR-UWB) with an autocorrelation receiver (AcR) is a great technical challenge. Differing from the currently empirical design method of DL, in this paper a semi-analytic approach is proposed through Gaussian approximation of the expression for conditional bit error rate (BER), based on i...

Abstract. An eventual property of a matrix M ∈ C is a property that holds for all powers M, k ≥ k0, for some positive integer k0. Eventually positive and eventually nonnegative matrices have been studied extensively, and some results are known for eventually r-cyclic matrices. This paper introduces and establishs properties of eventually reducible matrices, establishs properties of the eigenstr...

We study the Eisenstein ideal for modular forms of even weight $k>2$ and prime level $N$. pay special attention to phenomenon extra reducibility: is strictly larger than cutting out reducible Galois representations. prove a modularity theorem these As consequences, we relate derivative Mazur–Tate $L$-function rank Hecke algebra, generalizing Merel, give new proof case an equivariant main conjec...

We consider the algebraic Riccati equation for which the four coefficient matrices form an M -matrix K. When K is a nonsingular M -matrix or an irreducible singular M -matrix, the Riccati equation is known to have a minimal nonnegative solution and several efficient methods are available to find this solution. In this paper we are mainly interested in the case where K is a reducible singular M ...

An eventual property of a matrix M ∈ C is a property that holds for all powers M, k ≥ k0, for some positive integer k0. Eventually positive and eventually nonnegative matrices have been studied extensively, and some results are known for eventually r-cyclic matrices. This paper introduces and establishs properties of eventually reducible matrices, establishs properties of the eigenstructure of ...