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New Bounds and Constructions for Constant Weighted X-Codes.
- Source :
- IEEE Transactions on Information Theory; Apr2021, Vol. 67 Issue 4, p2181-2191, 11p
- Publication Year :
- 2021
-
Abstract
- As a crucial technique for integrated circuits (IC) test response compaction, X-compact employs a special kind of codes called X-codes for reliable compressions of the test response in the presence of unknown logic values (Xs). From a combinatorial view point, Fujiwara and Colbourn introduced an equivalent definition of X-codes and studied X-codes of small weights that have good detectability and X-tolerance. An $({\it\text { m, n, d, x}})~\text {X}$ -code is an $\text {m}\times \text {n}$ binary matrix with column vectors as its codewords. The parameters ${\it\text { d, x}}$ correspond to the test quality of the code. In this paper, bounds and constructions for constant weighted X-codes are investigated. First, we obtain a general result on the maximum number of codewords n for an $({\it\text { m, n, d, x}})~\text {X}$ -code of weight w, and we further improve this lower bound for the case with $\text {x}=2$ and $\text {w}=3$ through the probabilistic method. Then, using tools from additive combinatorics and finite fields, we present some explicit constructions for constant weighted X-codes with $\text {d}=3,7$ and $\text {x}=2$ , which are optimal for the case when $\text {d}=3, \text {w}=4$ and nearly optimal for the case when $\text {d}=3,\text {w}=3$. We also consider a special class of X-codes introduced by Fujiwara and Colbourn and improve the best known lower bound on the maximum number of codewords for this kind of X-codes. [ABSTRACT FROM AUTHOR]
- Subjects :
- FINITE fields
INTEGRATED circuits
COMBINATORICS
COMPACTING
LOGIC
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 67
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 149417948
- Full Text :
- https://doi.org/10.1109/TIT.2021.3054612