# zbMATH — the first resource for mathematics

A note on matrix rigidity. (English) Zbl 0848.15005
A matrix is said to be rigid if any change in each of $$k$$ rows decreases the rank by no more than $$k$$ units. Generalizations of this notion are given. They apply especially when the underlying field $${\mathbf F}$$ is finite. The appropriate context is the theory of algebraic codes.

##### MSC:
 15A03 Vector spaces, linear dependence, rank, lineability 11T71 Algebraic coding theory; cryptography (number-theoretic aspects) 15B33 Matrices over special rings (quaternions, finite fields, etc.)
##### Keywords:
finite field; rank; theory of algebraic codes
Full Text:
##### References:
 [1] D. Y. Grigorjev:Notes of the Leningrad Branch of the Steklov Mathematical Institute of the Academy of Science of the USSSR,60 (1976), 38-48. [2] Pudlak, Savitzky, andA. Razborov: Observations on rigidity of Hadamard matrices, Personal Communication. [3] A. Razborov: On rigid matrices,Problems of Pure and Applied Mathematics (Literal Translation from Russian), to appear. · Zbl 0770.68073 [4] L. G. Valiant: Graph-theoretic arguments in low-level complexity. Technical Report, University of Edinburgh, 1977. Computer Science Report 13-77. Also in Proc. 6th Symp. on Mathematical Foundations of Computer Science, Tatranska Lomnica, Czechoslovakia 1978. [5] G. van der Geer, andJ. van Lint:Introduction to Coding Theory and Algebraic Geometry, Birkhäuser Verlag, Boston, 1988. · Zbl 0648.94012 [6] J. van Lint:Introduction to Coding Theory, Springer-Verlag, New York, 1982. · Zbl 0485.94015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.