Abstract
In the present work, the class of metrics connected with subsets of the linear space on the field, GF(2), is considered and a number of facts are established, which allow us to express the correcting capacity of codes for the additive channel in terms of this metrics. It is also considered a partition of the metric space, Bn, by means of D-representable codes. The equivalence of D-representable and the perfect codes in the additive channel is proved.
Highlights
The class of metrics connected with subsets of the linear space on the field, GF(2), is considered and a number of facts are established, which allow us to express the correcting capacity of codes for the additive channel in terms of this metrics
It is considered a partition of the metric space, Bn, by means of D-representable codes
The “noise” generated by the additive channel leads to the fact that there appears a word at the outlet of the channel which is different from that at its inlet
Summary
The “noise” generated by the additive channel leads to the fact that there appears a word at the outlet of the channel which is different from that at its inlet. In connection with this there rises a necessity of transforming (coding) information for conducting it through the given channel, as well as a necessity of retransforming (decoding) it at the channel outlet. This circumstance makes one introduce such standard notions in the coding theory as: error correcting code; transfer/decoding speed, etc. The equivalence of D -representable and perfect codes in the additive channel is proved
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