```ts
/**
 * Encodes strings using run-length encoding.
 *
 * @param {string} input - The string to encode.
 * @returns {string} - The encoded string.
 */
export function runLengthEncode(input: string): string {
  if (typeof input !== 'string') {
    throw new Error("Input must be a string.");
  }

  let result = '';
  for (let i = 0; i < input.length; i++) {
    const character = input[i];
    let count = 1;

    while (i + 1 < input.length && input[i] === input[i + 1]) {
      i++;
      count++;
    }

    result += `${character}${count.toString().padStart(2, '0')}`;
  }

  return result;
}
```