In
coding theory
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are stud ...
, Srivastava codes, formulated by Professor
J. N. Srivastava
Jagdish Narain Srivastava (1933-2010) was an Indian-born mathematician, statistician and a professor at Colorado State University. Srivastava is known for the research in the area of Design of experiments, Multivariate analysis and Combinatorial ma ...
, form a class of parameterised
error-correcting codes
In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea is ...
which are a special case of
alternant code
In coding theory, alternant codes form a class of parameterised error-correcting codes which generalise the BCH codes.
Definition
An ''alternant code'' over GF(''q'') of length ''n'' is defined by a parity check matrix ''H'' of alternant form ''H ...
s.
Definition
The original ''Srivastava code'' over GF(''q'') of length ''n'' is defined by a parity check matrix ''H'' of
alternant form
:
where the α
''i'' and ''z''
''i'' are elements of GF(''q''
''m'')
Properties
The parameters of this code are length ''n'', dimension ≥ ''n'' − ''m''s and minimum distance ≥ s + 1.
References
*
Error detection and correction
Finite fields
Coding theory
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