Griesmer Type Bounds for Nonlinear Codes and Their Applications

Abstract

In this paper, we propose three Griesmer type bounds for the minimum Hamming weight of complementary codes of linear codes. Infinite families of complementary codes meeting the three Griesmer type bounds are given to show these bounds are tight. The Griesmer type bounds proposed in this paper are significantly stronger than the classical Griesmer bound for linear codes. As a by-product, we construct some optimal few-weight codes and determine their weight distributions. As an application, Griesmer type bounds for the column distance of convolutional codes are presented. These Griesmer type bounds are stronger than the Singleton bound for convolutional codes.