Quasi-cyclic subcodes of cyclic codes

We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration is equivalent to enumeration of certain vector subspaces in finite fields. In particular, we present enumeration results for quasi-cyclic subcodes of the simplex code and duals of certain BCH codes. Our results are based on the trace representation of cyclic codes

Paradigms for Parameterized Enumeration

The aim of the paper is to examine the computational complexity and algorithmics of enumeration, the task to output all solutions of a given problem, from the point of view of parameterized complexity. First we define formally different notions of efficient enumeration in the context of parameterized complexity. Second we show how different algorithmic paradigms can be used in order to get parameter-efficient enumeration algorithms in a number of examples. These paradigms use well-known principles from the design of parameterized decision as well as enumeration techniques, like for instance kernelization and self-reducibility. The concept of kernelization, in particular, leads to a characterization of fixed-parameter tractable enumeration problems.Comment: Accepted for MFCS 2013; long version of the pape

Enumeration in Alzheimer's disease and other late life psychiatric syndromes

Previous studies suggest that visual enumeration is spared in normal aging but impaired in abnormal aging (late stage Alzheimer's disease, AD), raising the task's potential as a marker of dementia. Experiment 1 compared speeded enumeration of 1–9 random dots in early stage AD, vascular dementia (VAD), depression, and age-matched controls. Previous deficits were replicated but they were not specific to AD, with the rate of counting larger numerosities similarly slowed relative to controls by both AD and VAD. Determination of subitizing span was complicated by the surprisingly slower enumeration of one than of two items, especially in AD patients. Experiment 2 showed that AD patients’ relative difficulty with one item persisted with further practice and extended to the enumeration of targets among distractors. However, it was abolished when pattern recognition was possible (enumerating dots on a die). Although an enumeration test is unlikely to help differentiate early AD from other common dementias, the unexpected pattern of patients’ performance challenges current models of enumeration and requires further investigation

Modulating attentional load affects numerosity estimation: evidence against a pre-attentive subitizing mechanism

Traditionally, the visual enumeration of a small number of items (1 to about 4), referred to as subitizing, has been thought of as a parallel and pre-attentive process and functionally different from the serial attentive enumeration of larger numerosities. We tested this hypothesis by employing a dual task paradigm that systematically manipulated the attentional resources available to an enumeration task. Enumeration accuracy for small numerosities was severely decreased as more attentional resources were taken away from the numerical task, challenging the traditionally held notion of subitizing as a pre-attentive, capacity-independent process. Judgement of larger numerosities was also affected by dual task conditions and attentional load. These results challenge the proposal that small numerosities are enumerated by a mechanism separate from large numerosities and support the idea of a single, attention-demanding enumeration mechanism

Further evidence on the effect of symbolic distance on Stroop-like interference

Pavese and Umiltà found that, in an enumeration task, Stroop-like interference is larger when the digit identity is symbolically close to the enumeration response than when it is symbolically far. In two experiments testing 49 undergraduates, we further explored this phenomenon using Francolini and Egeth's paradigm. We found that symbolic distance affected interference even when the stimulus was briefly presented and masked. In Exp. 2, which tested numerosities outside the subitizing range, individuals used a different enumeration strategy but showed the same symbolic distance effect. These results support the hypothesis that Stroop interference found in enumeration tasks depends on a rapid and automatic activation of digits' magnitude representation