CODES OF LENGTH tn INVARIANT UNDER ROTATIONS OF ORDER n

Embodiments include generating an error correction code by identifying two error-correcting codes of length n with minimum distances d and 2d, such that the second code is contained into the first code. Data is then encoded into t−1 blocks using the first code, and into the t-th block using the second block. The first t−1 encoded blocks are stored into t−1 blocks of memory locations, while the exclusive-OR (XOR) of such t−1 encoded blocks and the t-th encoded block is stored into a t-th block of memory location. The final encoded vector of length to is identified as belonging in a code with minimum distance 2d. Rotations of an encoded vector jn times are identified as belonging to the same equivalence class. A received vector or its rotations jn times can be successfully identified in the presence of up to d−1 errors, while d errors are identified as uncorrectable errors.