Designing of Variable Distance Linear Block Codes with High Code Rate

Developing long codes with high levels of error correction capability has been one of the most difficult issues in coding theory. This research introduces an alternative way to create a new type of Increased Distance Linear Block Code (IDLBC). This code has a code rate greater than 1/2. The IDLBC starts with the creation of a generator matrix by using an Upper Triangular Matrix (UTM) and constructing one Linear Block Code (LBC) that has Distance-Preserving Mapping (DPM) property for any (n, k) combinations. Afterwards, an algorithm is used to change the UTM of the generator matrix to give a code with a Distance-Increasing Mapping (DIM) property. The performance of the code is then enhanced using code puncturing to produce a code having a code rate of more than 1/2, but maintaining the improved performance for Bit Error Rate (BER). It is clear that the codes being developed in this paper are superior to the traditional Hamming Codes. The transition from DPM to DIM gives codes with improved distance performance, leading to more reliable performance.