A scheme for storing information in a memory system with defective memory ceils using "additive" codes was proposed by Kuznetsov and Tsybakov. When a source message is to be stored in a memory with defective cells, a code vectorxmasking the defect pattern of the memory is formed by adding a vector defined by the message and the defect pattern to the encoded message, and thenxis stored. The decoding process does not require the defect information. Considerably better bounds on the information rate of codes of this type which are capable of masking multiple defects and correcting multiple temporary errors are presented. The difference between the upper and lower bounds approaches the difference between the known best upper and lower bounds for random error correcting linear codes as the word length becomes large. Examples of efficient codes for masking double or fewer defects and correcting multiple temporary errors are presented.