We define, construct and sketch possible applications of a new class of non-linear codes: co-orthogonal codes. The advantages of these codes are twofold: first, it is easy to decide whether two codewords form a unique pair (this can be used in decoding information or identifying users of some not-publicly-available or non-free service on the Internet or elsewhere), and the identification process of the unique pair can be distributed between entities, who perform easy tasks, and only the information, gathered from all of them would lead to the result of the identifying process: the entities, taking part in the process will not have enough information to decide or just to conjecture the outcome of the identification process.
Moreover, we describe a fast (and general) method for generating (non-linear) codes with prescribed dot-products with the help of multi-linear polynomials.
Keywordsnon-linear codes co-orthogonal codes codes and set-systems multi-linear polynomials composite modulus
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