Vedic Literature > Mathematics > Error correcting code > Vikratis or Encoder

Consider a RV verse labeled M having m words, M = a1,a2,a3,…,am, each ai being a distinct word. Note two consecutive words ai and ai+1 are always different from each other. The idea of error correcting code-like vikratis is given below.  It has two boxes, the encoder and decoder. It should be noted that both encoder operations and decoder  operations are carried out mentally without using mechanical gadgets. We use these words because of their familiarity in modern parlance.

For the given verse M, the encoder generates a verse I  having n words, n being much greater than m. The words of I are those in M. The chanter recites I unconsciously,  introducing errors. The output heard by a listener is, O = O1,…,On, having n words, n being known. Thus, O # I.

(# - Not equal to)

With every M, a string I is generated , having the same words as in M; the length of I being 4m or more. The rules for generating the verse I should be such that I can be chanted with relative ease. The verse I is chanted by a reciter. Typically, he or she memorises all the encoded versions of all the verses in one mandala or chapter of Rig Veda. Hence errors are bound to creep in. The version of I heard is called  O, which may have errors. Another expert in the same family, on hearing O, acts as a (mental) decoder and generates the correct verse M, under appropriate conditions.

There are eight families of vikratis with suggestive names like maala (garland), ratha (chariot), danda (stick), dvaja (flag). Each family has several variants. We give below a variant of the garland or maala family, Krama-maala.

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