Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...

Stabilizer codes obtained via the CSS code construction and the Steane’s enlargement of subfield-subcodes and matrix-product codes coming from generalized ReedMuller, hyperbolic and affine variety codes are studied. Stabilizer codes with good quantum parameters are supplied, in particular, some binary codes of lengths 127 and 128 improve the parameters of the codes in http://www.codetables.de. ...

Economic system mathematical model often contains multiple variance change points about structure model. In the same mean, we combine the Bayesian method with the maximum likelihood method on the detection of the variance multiple change points. With Bayesian method, we can eliminate extra parameters first, and then use maximum likelihood method to find the change position. So we both can elimi...

the binary and ternary codes spanned by the rows of the point by block incidence matrices of some 2-designs and their complementary and orthogonal designs are studied. a new method is also introduced to study optimal codes.

Co-movement between futures prices can arise when commodities are substitutes. Using Johansen’s co-integration procedure, we fail to find a significant long-run link between soybean and corn prices on the Dalian Commodity Exchange of China. This relationship is re-examined using Johansen’s co-integration procedure that permits structural breaks. Results show evidence of co-integration and...