A Brief Encounter with Linear Codes

While studying irreducible polynomials and fields our abstract algebra professor briefly mentioned that they play a role in error correcting and detecting codes. It was this comment that fostered the idea of further study on this topic. It would give us the opportunity to to apply some abstract concepts to the physical realm. The information contained herein is from researching the topic. Most of the material relies upon matrices and polynomials. While it is brief in nature it does lay a simple foundation of the some basic concepts of linear block blocks along with a subset known as cyclic codes. These cyclic codes have a great deal of structure and we further bring the abstract into the physical world by showing how cyclic codes can be implemented in hardware. The information here is just the tip of iceberg so there is so much more!