 uniformly distributed source. The maximum entropy of a 26-character source, which cannot be surpassed, is thus Hmax = I(1/26) = log 26 = 4.700 bit/symbol. We see from the result that our European languages are not too far from the maximum entropy limit, namely, within 85% to 88% of this absolute reference. As described in forthcoming chapters, there exist different possibilities of coding language alphabets Entropy Table 4.2 Alphabetical source entropies H of English, German, French, Italian, Spanish, and Portuguese, and the corresponding ten most frequent characters. H (bit/symbol) Ten most frequent characters English 4.147 ETOANIRSHD German 4.030 ENIRSTADUH French 4.046 EAISTNRULO Italian 3.984 EAIONLRTSC Spanish 4.038 EAOSNIRLDU Portuguese 3.991 AEOSRINDTM German French Italian Spanish Portuguese English symbol-character probability (%) Figure 4.4 Correlation between English character symbols with that of other European languages, according to data shown in Fig. 4.3. with more compact symbols, or codewords, in such a way that the coded language source may approach this entropy limit. Table 4.2 also reveals that there exist substantial differences between the ten most frequent symbol characters. Note that this (1956) survey yields for English the sequence ETOANIRSHD, while the earlier data (1941) shown in Fig. 4.2 yields the sequence ETAONRISHD. This discrepancy is, however, not significant considering that the prob- ability differences between A and O and between R and I are between 0.1% and 0.4%, which can be considered as an effect of statistical noise. The most interesting side of 4.3 Language entropy these character hierarchies is that they can provide information as to which language is used in a given document, in particular if the document has been encrypted according to certain coding rules (this is referred to as a ciphertext). The task of decryption, recover- ing what is referred to as the plaintext, is facilitated by the analysis of the frequencies (or probabilities) at which certain coded symbols 