High-rate self-synchronizing codes

Self-synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization. Difference systems of sets are combinatorial designs which specify the positions of synchronization markers in codewords in such a way that the resulting error-tolerant self-synchronizing codes may be realized as cosets of linear codes. Ideally, difference systems of sets should sacrifice as few bits as possible for a given code length, alphabet size, and error-tolerance capability. However, it seems difficult to attain optimality with respect to known bounds when the noise level is relatively low. In fact, the majority of known optimal difference systems of sets are for exceptionally noisy channels, requiring a substantial amount of bits for synchronization. To address this problem, we present constructions for difference systems of sets that allow for higher information rates while sacrificing optimality to only a small extent. Our constructions utilize optimal difference systems of sets as ingredients and, when applied carefully, generate asymptotically optimal ones with higher information rates. We also give direct constructions for optimal difference systems of sets with high information rates and error-tolerance that generate binary and ternary self-synchronizing codes.Comment: 9 pages, no figure, 2 tables. Final accepted version for publication in the IEEE Transactions on Information Theory. Material presented in part at the International Symposium on Information Theory and its Applications, Honolulu, HI USA, October 201

Gamma-ray spectrometry in the field: Radioactive heat production in the Central Slovakian Volcanic Zone

We report 62 sets of measurements from central-southern Slovakia, obtained using a modern portable gamma-ray spectrometer, which reveal the radioactive heat production in intrusive and extrusive igneous rocks of the Late Cenozoic Central Slovakian Volcanic Zone. Sites in granodiorite of the Štiavnica pluton are thus shown to have heat production in the range ~ 2.2–4.9 μW m− 3, this variability being primarily a reflection of variations in content of the trace element uranium. Sites in dioritic parts of this pluton have a lower, but overlapping, range of values, ~ 2.1–4.4 μW m− 3. Sites that have been interpreted in adjoining minor dioritic intrusions of similar age have heat production in the range ~ 1.4–3.3 μW m− 3. The main Štiavnica pluton has zoned composition, with potassium and uranium content and radioactive heat production typically increasing inward from its margins, reflecting variations observed in other granodioritic plutons elsewhere. It is indeed possible that the adjoining dioritic rocks, hitherto assigned to other minor intrusions of similar age, located around the periphery of the Štiavnica pluton, in reality provide further evidence for zonation of the same pluton. The vicinity of this pluton is associated with surface heat flow ~ 40 mW m− 2 above the regional background. On the basis of our heat production measurements, we thus infer that the pluton has a substantial vertical extent, our preferred estimate for the scale depth for its downward decrease in radioactive heat production being ~ 8 km. Nonetheless, this pluton lacks any significant negative Bouguer gravity anomaly. We attribute this to the effect of the surrounding volcanic caldera, filled with relatively low-density lavas, ‘masking’ the pluton's own gravity anomaly. We envisage that emplacement occurred when the pluton was much hotter, and thus of lower density, than at present, its continued uplift, evident from the local geomorphology, being the isostatic consequence of localized erosion. The heat production in this intrusion evidently plays a significant role, hitherto unrecognized, in the regional geothermics

The q-ary image of some qm-ary cyclic codes: permutation group and soft-decision decoding

Using a particular construction of generator matrices of the q-ary image of qm-ary cyclic codes, it is proved that some of these codes are invariant under the action of particular permutation groups. The equivalence of such codes with some two-dimensional (2-D) Abelian codes and cyclic codes is deduced from this property. These permutations are also used in the area of the soft-decision decoding of some expanded Reed–Solomon (RS) codes to improve the performance of generalized minimum-distance decoding

Synthesis, X-Ray Diffraction (XRD), Differential Thermal Analysis (DTA), and Scanning Electron Microscopy (SEM) of the Alloy (CuInTe2)1-x(NbTe)x with x=0.5

A polycrystalline ingot (30mm long, 10mm diameter) of the alloy (CuInTe2)1-x(NbTe)x with x=0.5 has been produced using the melt and anneal technique and characterized by X-Ray Diffraction (XRD), Diferential Thermal Analysys (DTA) and Scanning Electron Microscopy (SEM). From XRD results, and using Rietveld refinement method, the crystal structure has been obtained indicating than this alloy crystallizes in a chalcopyrite-like structure, space group  (Nº 112), unit cell parameters a = 6.1933(2) Å, c = 12.4293(2) Å, V = 476.75(2) Å3, figures of merit Rexp= 6.7%, Rp= 7.5%, Rwp= 7.3%, and S = 1.1. DTA measurements indicate three thermal transitions at 1028, 977 and 886 K in the heating cycle, and 1016, 900 and 848 K in the cooling. The transitions at 1028 and 1016 correspond to the melting and solidification point, respectively; the transitions at 977 and 900 K are of solid to liquid+solid type, whereas the transitions at 886 and 848 K correspond to order-disorder. The melting point is incongruent. In the diffraction pattern, traces of a secondary phase are observed; this phase has been identified using SEM technique as (CuIn)0.5NbTe2. DOI: http://dx.doi.org/10.17807/orbital.v14i1.167