**Abstract. **
The
article discusses the spectral encoding based conversion of Christenson over the
field GF(4). The purpose of the encoding is error detection. The effectiveness
of encoding is evaluated in the case when the number of errors in code word
larger than the number of guaranteed detectable errors. Simulation
of the decoding process
showed that
the highest value of the probability of
undetected error is obtained
when the number of errors
in the code word
equal to the code
distance.
This probability is
used in the article
to estimate
from above
the probability of undetected error.
If the
number of errors in the code word
is greater than or equal to
the code distance, the increase of
the length of the
code words under the condition of
constant value of the code distance gives the
opportunity to obtain an acceptable value
of probability of undetected error.

**Key words:** spectral encoding, error detection, transformation of
Christenson.

**References**

1.
Mutter, V. M. *Osnovy pomekhoustoichivoi
teleperedachi informatsii.* [Fundamentals of error-correcting information
transmission].– St-Petersburg, Energoatomizdat Publ. 1990. 288 p. (In Russian)

2. *Peredacha
discretnykh soobschenii* [Transmission of
discrete messages] / Vershinin V. A. Rybinsk state aviation technological Academy
them. P.
A. Solovyov. Rybinsk, 2002.– 82 p.– Dep. in
VINITI 17.12.2002,
¹.
2196-Â2002
(In Russian)