Fast Erasure-and-Error Decoding and Systematic Encoding of a Class of Affine Variety Codes

In this paper, a lemma in algebraic coding theory is established, which is frequently appeared in the encoding and decoding for algebraic codes such as Reed-Solomon codes and algebraic geometry codes. This lemma states that two vector spaces, one corresponds to information symbols and the other is indexed by the support of Grobner basis, are canonically isomorphic, and moreover, the isomorphism is given by the extension through linear feedback shift registers from Grobner basis and discrete Fourier transforms. Next, the lemma is applied to fast unified system of encoding and decoding erasures and errors in a certain class of affine variety codes.Comment: 6 pages, 2 columns, presented at The 34th Symposium on Information Theory and Its Applications (SITA2011

Lemma for Linear Feedback Shift Registers and DFTs Applied to Affine Variety Codes

In this paper, we establish a lemma in algebraic coding theory that frequently appears in the encoding and decoding of, e.g., Reed-Solomon codes, algebraic geometry codes, and affine variety codes. Our lemma corresponds to the non-systematic encoding of affine variety codes, and can be stated by giving a canonical linear map as the composition of an extension through linear feedback shift registers from a Grobner basis and a generalized inverse discrete Fourier transform. We clarify that our lemma yields the error-value estimation in the fast erasure-and-error decoding of a class of dual affine variety codes. Moreover, we show that systematic encoding corresponds to a special case of erasure-only decoding. The lemma enables us to reduce the computational complexity of error-evaluation from O(n^3) using Gaussian elimination to O(qn^2) with some mild conditions on n and q, where n is the code length and q is the finite-field size.Comment: 37 pages, 1 column, 10 figures, 2 tables, resubmitted to IEEE Transactions on Information Theory on Jan. 8, 201

Decoding of Projective Reed-Muller Codes by Dividing a Projective Space into Affine Spaces

A projective Reed-Muller (PRM) code, obtained by modifying a (classical) Reed-Muller code with respect to a projective space, is a doubly extended Reed-Solomon code when the dimension of the related projective space is equal to 1. The minimum distance and dual code of a PRM code are known, and some decoding examples have been represented for low-dimensional projective space. In this study, we construct a decoding algorithm for all PRM codes by dividing a projective space into a union of affine spaces. In addition, we determine the computational complexity and the number of errors correctable of our algorithm. Finally, we compare the codeword error rate of our algorithm with that of minimum distance decoding.Comment: 17 pages, 4 figure

Effective colloidal processing for densification before SPS

In conventional dry processing, fine particles tend to agglomerate spontaneously due to Van der Waals attractive forces. Since the agglomeration of particles forms large residual pores in green bodies, elevated temperatures are necessary for densification. Colloidal processing is a very effective technique for controlling the pore size distribution in green compacts before sintering. The green compacts having small residual pores with a narrow size distribution is expected to enhance the densification at low sintering temperature during SPS. We already reported that colloidal processing for controlling the packing structure in green compact is effective for densification in SPS in the case of SiC. A commercially available SiC (6H) powder with the average particle size of 0.55 mm was used as the starting materials. When using the dry processing for consolidation, the density of the sample sintered by SPS in a vacuum atmosphere at 1950°C was 92% of the theoretical value. Aqueous suspensions with dispersed particles were prepared by adjusting pH and consolidated by slip casting to prepare the dense green compacts. The relative density of SiC prepared by SPS was increased with increasing temperature and reached more than 97% at 1950°C as shown in Fig. 1. In this presentation, this processing was applied to fabrication of transparent alumina. Commercially available Al2O3 powder with the average particle size of 0.4 mm was used as the starting materials. Suspensions with 30 vol% solid were consolidated by slip casting. The green compacts before sintering were further densified by cold isostatic pressing at 392 MPa for 10 min and calcined at 500°C for 1 h in air in order to burn off the dispersant. Final sintering was carried out at 1150°C under a uniaxial pressure of 100 MPa using an SPS. After rapid heating to 600°C, the temperature was raised from 600°C to 1150°C using a heating rate of 5°C/min. After holding samples at the sintering temperature for 10 min and then subsequently annealing them at 1000°C for 10 min, we obtained a sintered disk with a diameter of 25 mm and a thickness of 2 mm. Fig. 2(a) shows the photograph of the sample from the green compact prepared by slip casting, Fig2(b) is the sample densified by SPS from the as-received powder directly. The transparency of the sample prepared by slip casting is clearer than that of the sample by SPS from the as-received powder directly. Please click Additional Files below to see the full abstract

Positive chemotaxis to plant apoplastic fluids of Pseudomonas syringae pv. tabaci 6605 and metabolome analysis

Pseudomonas syringae pv. tabaci 6605 (Pta6605) is a causal agent of wildfire disease in host tobacco plants. Although chemotaxis has been shown to be necessary for Pta6605 in tobacco infection, the chemoattractants at the site of infection are unclear. Pta6605 was attracted to the apoplastic fluid from not only host tobacco leaves but also non-host plant leaves, indicating that Pta6605 is attracted to common plant metabolites. Metabolome analysis of apoplastic fluid from tobacco leaves revealed that amino acids including γ-aminobutyric acid and organic acids are abundant, suggesting that these compounds are potential chemoattractants

Taurine supplementation enhances endurance capacity by delaying blood glucose decline during prolonged exercise in rats

Taurine enhances physical performance; however, the underlying mechanism remains unclear. This study examined the effect of taurine on the overtime dynamics of blood glucose concentration (BGC) during endurance exercise in rats. Male F344 rats were subjected to transient treadmill exercise until exhaustion following 3 weeks of taurine supplementation or non-supplementation (TAU and CON groups). Every 10 min during exercise, BGC was measured in blood collected through cannulation of the jugular vein. Gluconeogenesis-, lipolysis-, and fatty acid oxidation-related factors in the plasma, liver, and skeletal muscles were also analyzed after 120-min run. Exercise time to exhaustion was significantly longer with taurine supplementation. BGC in the two groups significantly increased by 40 min and gradually and significantly decreased toward the respective exhaustion point. The decline in BGC from the peak at 40 min was significantly slower in the TAU group. The time when the once-increased BGC regressed to the 0-time level was significantly and positively correlated with exercise time until exhaustion. At the 120-min point, where the difference in BGC between the two groups was most significant, plasma free fatty acid concentration and acetyl-carnitine and N-acetyltaurine concentrations in skeletal muscle were significantly higher in the TAU group, whereas glycogen and glucogenic amino acid concentrations and G6Pase activity in the liver were not different between the two groups. Taurine supplementation enhances endurance capacity by delaying the decrease in BGC toward exhaustion through increases of lipolysis in adipose tissues and fatty acid oxidation in skeletal muscles during endurance exercise