Technical Program

Paper Detail

Paper Title On the Maximum Number of Codewords of X-Codes of Constant Weight Three
Paper IdentifierWE2.R9.5
Authors Yu Tsunoda, Yuichiro Fujiwara, Chiba University, Japan
Session Bounds on Codes
Location Pontoise, Level 5
Session Time Wednesday, 10 July, 11:40 - 13:20
Presentation Time Wednesday, 10 July, 13:00 - 13:20
Manuscript  Click here to download the manuscript
Abstract 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 $d \geq 2$ 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.