On efficient majority logic decodable codes

Abstract

A particular shortening technique is applied to majority logic decodable codes of length 2^{t} . The shortening technique yields new efficient codes of lengths n = 2^{p} , where p is a prime, e.g., a (128,70) code with d_{maj} = 16 . For moderately long code lengths (e.g., n = 2^{11} or 2^{13}) , 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 n = 2^{m} where m is a composite number, for example, a (512,316) code with d_{maj} = 32 code which has 42 more information bits than the previously most efficient majority logic decodable code.