The standard erasure codes (polynomial ones) require that the field size (so alphabet size) is larger than the number of symbols in the codeword. Clearly we can have arbitrarily-close-to-ideal erasure codes even for smaller alphabet sizes (because noisy coding theorem). Are there some that can be easily described?
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Haven't found an answer I'd be satisfied with. The simplest way I know of right now is picking a random high density parity code (with the downside of the necessity for randomness in the code's construction and high but still polynomial time complexity of decoding).
