There will be two cases here:

A) When u assign a one letter code:
There ar 26 alphabets so these can be assigned to 26 different players .

B) When u assign a two letter code :
Here the two letter code will be 26C1*25C1(since first letter will have two be chosen among the 26 alphabets for the second letter you will have on eless alphabet to choose from hence u will have to choose a alphabet among remaining 25 ones)
Now in the above case there will be repetations like AB and BA which is not allowed as per the question.
Hence total possible ways for two alphabet word without repetation is (26C1*25C1)/2=325.

Hence the total no. of ways is 26+325=351 i.e.Ans B