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Message Authentication Codes (MACs) are very sensitive to any modification in the message. The verification fails even if there is a slight change in the message. However, special algorithms have been introduced that tolerate a small amount of noise in messages as required by some applications. Noise Tolerant Message Authentication Code (NTMAC) is an example of noise tolerant authenticator algorithm. NTMAC is block oriented and unlike MAC it localizes errors at the block level. Nevertheless, there is no efficient way for correcting erroneous blocks by NTMAC. This paper presents a novel algorithm as an enhancement of NTMAC, called the Error Correcting - NTMAC (EC-NTMAC) and a variant of EC-NTMAC, called the Error Correcting - Weighted NTMAC (EC-WNTMAC). EC-NTMAC introduces error correction of erroneous blocks and EC-WNTMAC extends EC-NTMAC to the correction of blocks based on their importance level or the so called weight. The later approach makes the EC-NTMAC more suitable for some applications like image and multimedia communications where few errors are acceptable. Simulation results, showing capabilities of both of the proposed algorithms as well as the performance and security considerations are given in the paper.