We consider linear error correcting codes associated to higher-dimensional projective varieties defined over a finite field. The problem of determining the basic parameters of such codes often leads to some interesting and difficult questions in combinatorics and algebraic geometry. This is illustrated by codes associated to Schubert varieties in Grassmannians, called Schubert codes, which have...

Informally, an error-correcting code has “nice” listdecodability properties if every Hamming ball of “large” radius has a “small” number of codewords in it. Here, we report linear codes with non-trivial list-decodability: i.e., codes of large rate that are nicely listdecodable, and codes of large distance that are not nicely list-decodable. Specifically, on the positive side, we show that there...

Digital image watermarking is one of the effective schemes to protect copyrights still images. However, existing are not robust enough common geometric transformation attacks such as arbitrary rotation, scaling and shifting with desirable hiding capacity. To address this issue, we propose a scheme based on correction codes (GCCs). In scheme, watermark pre-set GCCs combined embedded into cover o...

We apply various seq2seq models on programming language correction tasks Juliet Test Suite for C/C++ and Java of Software Assurance Reference Datasets achieve 75% (for C/C++) 56% Java) repair rates these tasks. introduce pyramid encoder in models, which significantly increases the computational efficiency memory efficiency, while achieving similar rate to their nonpyramid counterparts. successf...