Systems and methods for dynamically encoding and decoding binary numbers using linear-time algorithms that encode and decode Hamming Distance-Based representations for the binary numbers are described. The binary numbers may correspond with integer values, such as 64-bit, 128-bit, or 256-bit integer values. In some cases, in response to detecting that a binary number is to be stored using a particular type of memory (e.g., a phase change memory), the binary number may first be encoded using a Hamming Distance-Based representation and then the encoded data may be written to the particular type of memory. The binary number may be encoded by generating a binary string or a binary array representing the binary number such that if one bit flips within the binary string or the binary array, the maximum distortion in the number is less than a threshold amount (e.g., less than 256).