11,813 research outputs found

### Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound

It was shown by Massey that linear complementary dual (LCD for short) codes
are asymptotically good. In 2004, Sendrier proved that LCD codes meet the
asymptotic Gilbert-Varshamov (GV for short) bound. Until now, the GV bound
still remains to be the best asymptotical lower bound for LCD codes. In this
paper, we show that an algebraic geometry code over a finite field of even
characteristic is equivalent to an LCD code and consequently there exists a
family of LCD codes that are equivalent to algebraic geometry codes and exceed
the asymptotical GV bound

### Taxation and Transaction Costs in a General Equilibrium Asset Economy

Most financial asset pricing models assume frictionless, competitive markets that imply the absence of arbitrage opportunities. Given the absence of arbitrage opportunities and complete asset markets, there exists a unique martingale measure that implies martingale pricing formulae and replicating asset portfolios. In incomplete markets, or markets with transaction costs, these results must be modified to admit non-unique measures and the possibility of imperfectly replicating portfolios. Similar difficulties arise in markets with taxation. Some theoretical research has argued that some taxation functions will imply arbitrage opportunities and the non-existence of a competitive asset economy. In this paper, we construct a multi-period, discrete time/state general equilibrium model of asset markets with transaction costs and taxes. The transaction cost technology and the tax system are quite general, so that we can include most discrete time/state models with transaction costs and taxation. We show that a competitive equilibrium exists. Our results require careful modeling of the government budget constraints to rule out tax arbitrage possibilities.Taxation, Transaction Costs, General Equilibrium, Asset Economy

### The signatures of the new particles $h_2$ and $Z_{\mu\tau}$ at e-p colliders in the $U(1)_{L_\mu-L_\tau}$ model

Considering the superior performances of the future e-p colliders, LHeC and
FCC-eh, we discuss the feasibility of detecting the extra neutral scalar
$h_{2}$ and the light gauge boson $Z^{}_{\mu\tau}$, which are predicted by the
${U(1)}_{L^{}_{\mu} - L^{}_{\tau}}$ model. Taking into account the experimental
constraints on the relevant free parameters, we consider all possible
production channels of $h_{2}$ and $Z^{}_{\mu\tau}$ at e-p colliders and
further investigate their observability through the optimal channels in the
case of the beam polarization P($e^{-}$)= -0.8. We find that the signal
significance above 5$\sigma$ of $h_{2}$ as well as $Z^{}_{\mu\tau}$ detecting
can be achieved via
$e^{-}p\to{e^{-}jh_{2}(\to{Z_{\mu\tau}Z_{\mu\tau}})}\to~e^{-}j+/\!\!\!\!{E}^{}_{T}$
process and a 5$\sigma$ sensitivity of $Z^{}_{\mu\tau}$ detecting can be gained
via
$e^{-}p\to{e^{-}jh_{1}(\to{Z^{}_{\mu\tau}Z^{}_{\mu\tau}})\to}~e^{-}j+/\!\!\!\!{E}^{}_{T}$
process at e-p colliders with appropriate parameter values and a designed
integrated luminosity. However, the signals of $h_{2}$ decays into pair of SM
particles are difficult to be detected.Comment: 22 pages, 9 figures, references added and typos are correcte

### Erasure List-Decodable Codes from Random and Algebraic Geometry Codes

Erasure list decoding was introduced to correct a larger number of erasures
with output of a list of possible candidates. In the present paper, we consider
both random linear codes and algebraic geometry codes for list decoding erasure
errors. The contributions of this paper are two-fold. Firstly, we show that,
for arbitrary $00$ ($R$ and $\epsilon$ are independent),
with high probability a random linear code is an erasure list decodable code
with constant list size $2^{O(1/\epsilon)}$ that can correct a fraction
$1-R-\epsilon$ of erasures, i.e., a random linear code achieves the
information-theoretic optimal trade-off between information rate and fraction
of erasure errors. Secondly, we show that algebraic geometry codes are good
erasure list-decodable codes. Precisely speaking, for any $0<R<1$ and
$\epsilon>0$, a $q$-ary algebraic geometry code of rate $R$ from the
Garcia-Stichtenoth tower can correct
$1-R-\frac{1}{\sqrt{q}-1}+\frac{1}{q}-\epsilon$ fraction of erasure errors with
list size $O(1/\epsilon)$. This improves the Johnson bound applied to algebraic
geometry codes. Furthermore, list decoding of these algebraic geometry codes
can be implemented in polynomial time

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