Optimal equitable symbol weight codes for power line communications

The use of multiple frequency shift keying modulation with permutation codes addresses the problem of permanent narrowband noise disturbance in a power line communications (PLC) system. Equitable symbol weight codes was recently demonstrated to optimize the performance against narrowband noise in a general coded modulation scheme. This paper establishes the first infinite family of optimal equitable symbol weight codes with code lengths greater than alphabet size and whose relative narrowband noise error-correcting capabilities do not diminish to zero as the length grows. These families of codes meet the Plotkin bound. The construction method introduced is combinatorial and reveals interesting interplay with an extension of the concept of generalized balanced tournament designs from combinatorial design theory.