We give bounds for the minimal distance of duals of binary BCH codes in a range where the Carlitz-Uchiyama bound is trivial. This is done by estimating the number of points on certain curves over finite fields.

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 si...

A bstract We extend existing results for the Nielsen complexity of scalar primaries and spinning in four dimensions by including supersymmetry. Specifically, we study circuits that transform a superconformal primary with definite scaling dimension, spin R-charge means continuous unitary gates from $$ \mathfrak{su} su </m...

Motivated by questions in property testing, we search for linear error-correcting codes that have the “single local orbit” property: i.e., they are specified by a single local constraint and its translations under the symmetry group of the code. We show that the dual of every “sparse” binary code whose coordinates are indexed by elements of F2n for prime n, and whose symmetry group includes the...

Multi-level cell (MLC) NAND flash memories are popular storage media because of their power efficiency and large storage density. Conventional reliable MLC NAND flash memories based on BCH codes or Reed-Solomon (RS) codes have a large number of undetectable and miscorrected errors. Moreover, standard decoders for BCH and RS codes cannot be easily modified to correct errors beyond their error co...

Love, Jeffrey A., Neil W. Richards, Chung Owyang, and David C. Dawson. Muscarinic modulation of voltagedependent Ca21 channels in insulin-secreting HIT-T15 cells. Am. J. Physiol. 274 (Gastrointest. Liver Physiol. 37): G397– G405, 1998.—Potentiation of insulin secretion from pancreatic b-cells by acetylcholine requires ongoing cyclic electrical activity initiated by other depolarizing secretagog...

Abnormal hypermethylation of CpG islands associated with tumor suppressor genes can lead to repression of gene expression and contribute significantly to tumorigenesis. Esophageal squamous cell carcinoma (ESCC) is thought to be developed through a multi-stage process, which involves basal cell hyperplasia (BCH), dysplasia (DYS), carcinoma in situ (CIS) and carcinoma. In the present study, we st...