CONSTRUCTION OF NEW CODES

In this paper, we introduce a new construction of codes, which we called Combined Construction, which allows the combination of codes with different properties (for example, a cyclic code with the ability to correct burst errors and a linear code with the ability to correct random errors), which can be combined together by direct sum. In this regard, we assume that there are several finite blocks of cyclic codes and, in order to make this structure more efficient, we combine them with a linear code that is not necessarily cyclic and study the properties of this code. By which we can obtain new codes with a greater rate from two given codes and also create a code with a larger Hamming distance or the ability to correct certain errors (for example, a combination of random and burst errors). We determine the structure of these combined codes giving the generator polynomials of these codes and we specify the form of their generator and parity check matrix. Our goal is to provide a new construction of codes, which can be a guide for researchers and engineers.

کلیدواژه ها:

Cyclic codes ، Construction codes ، Combined codes ، Linear codes