Perfect codes with respect to the LRTJ metric

Coding Theory is most important for data storage and data transfer to receivers especially in the information era we live in. There could be a lot of errors(noise) during information transfer by a channel. In this situation, receiver gets a different message than the sent message. The theory of Error Correcting Codes is used to determine and correct these errors. The theory of Error Correcting Codes aims to correct errors which occurs during information transmission by making some adjustments to original information to build a mathematical concept. If the errors which occur during the information transmission have a rule in the incidence way, a distance function can be defined. In this case, if distance function meets the conditions of a metric in mathematics, decoding can be done and the errors can be fixed according to the distances between messages. Perfect Codes correct all errors may occur during the information tramsmission and pack all space with error balls. For perfect codes, messages which are transfered by decoding are accesible, because information transmission quality is high. Hamming Metric is the first and most used metric to determine perfect codes . After that perfect code studies were, and still are done in different metrics. This study, we search for perfect codes with respect to the LRTJ metric. It is expected that this going to be a resource for a lot of studies concerning perfect codes and the LRTJ metric.