On efficient majority logic decodable codes

A particular shortening technique is applied to majority logic decodable codes of length . The shortening technique yields new efficient codes of lengths , where is a prime, e.g., a (128,70) code with . For moderately long code lengths (e.g., , a 20-25 percent increase in efficiency can be achieved over the best previously known majority logic decodable codes. The new technique also yields some efficient codes for lengths where is a composite number, for example, a (512,316) code with code which has 42 more information bits than the previously most efficient majority logic decodable code.