Physical Unclonable Functions (PUFs) present an attractive security primitive due to their volatile key generation capability. Subject to environmental conditions, the PUF response, however, is prone to errors which may undermine the reliability of the system when left unaddressed. An error-correction scheme is typically used alongside the PUF circuit when the PUF response is used as a key for cryptographic applications. In this paper, we propose the use of Cellular-Automata Error-Correcting Codes (CAECC) due to their simplicity and regularity. An efficient implementation of (15, 7, 5) CA-ECC encoder/decoder targeting a Xilinx Zynq-7000 device is demonstrated, and the design is validated on design compiler targeting 40nm TSMC technology. We also propose a skip-mode compact syndrome coding scheme for relaxed per-block BER. CAECC is tested in conjunction with the skip-mode scheme, and the approach is verified on ring oscillator PUF data. The skip-mode scheme is found to reduce the ring oscillator overhead up to 20% and enhance the entropy up to 23% compared to no-skip schemes.