English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

X-codes form a special class of linear maps which were originally introduced for data compression in VLSI testing and are also known to give special parity-check matrices for linear codes suitable for error-erasure channels. In the context of circuit testing, an (m, n, d, x) X-code compresses n-bit output data R from the circuit under test into m bits, while allowing for detecting the existence of an up to d-bit-wise anomaly in R even if up to x bits of the original uncompressed R are unknowable to the tester. Using probabilistic combinatorics, we give a nontrivial lower bound for any d &#x2265; 2 on the maximum number n of codewords such that an (m, n, d, 2) X-code of constant weight 3 exists. This is the first result that shows the existence of an infinite sequence of X-codes whose compaction ratio tends to infinity for any fixed d under severe weight restrictions. We also give a deterministic polynomial-time algorithm that produces X-codes that achieve our bound.

On the Maximum Number of Codewords of X-Codes of Constant Weight Three