Efficient error-correcting pooling designs constructed from pseudo-symplectic spaces over a finite field

Area of Science:

• Linear Algebra
• Coding Theory
• Finite Fields

Background:

• Disjunct matrices are crucial for efficient coding and testing.
• Pseudo-symplectic spaces provide a unique algebraic structure for matrix construction.

Purpose of the Study:

• To construct novel classes of t×n, s(e)-disjunct matrices.
• To analyze the test efficiency of these new matrix constructions.

Main Methods:

• Utilizing subspaces within the pseudo-symplectic space F(q)(²v +¹).
• Focusing on characteristic 2 field properties.
• Comparing derived test efficiency (t/n) with existing benchmarks.

Main Results:

• Successfully constructed two distinct classes of t×n, s(e)-disjunct matrices.
• Demonstrated that the test efficiency (t/n) of these new matrices is superior to that of D'yachkov et al. (2005).

Conclusions:

• The proposed matrix constructions offer enhanced test efficiency in coding theory.
• These findings contribute to the development of more efficient error-correcting codes.