System and method for generating cyclic codes for error control in digital communications

A system for generating cyclic codes for error control in digital communications, comprising:

• means for receiving a K-bit information signal represented by a polynomial U(x) having a degree K−1;
• means for transforming the information signal to form a transformed information signal, using a first transform represented by a polynomial G1(x) having a degree P, wherein P is greater than zero, the transformed information signal is represented by a polynomial T(x) having a degree K+P−1, and T(x) equals U(x)G1(x);
• means for generating an initial cyclic code represented by a polynomial R1(x) for the transformed information signal using a second transform represented by a polynomial G2(x), wherein R1(x) equals a remainder obtained by dividing T(x) by G2(x);
• and
• means for transforming the initial cyclic code to form a final cyclic code represented by a polynomial R2(x) using the first transform, wherein R2(x) equals R1(x)/G1(x).

A method for generating cyclic codes for error control in digital communications, comprising:

• (1) receiving a K-bit information signal represented by a polynomial U(x) having a degree K−1;
• (2) transforming the information signal to form a transformed information signal, using a first transform represented by a polynomial G1(x) having a degree P, wherein P is greater than zero, the transformed information signal is represented by a polynomial T(x) having a degree K+P−1, and T(x) equals U(x)G1(x);
• (3) generating an initial cyclic code represented by a polynomial R1(x) for the transformed information signal using a second transform represented by a polynomial G2(x), wherein R1(x) equals a remainder obtained by dividing T(x) by G2(x);
• and
• (4) transforming the initial cyclic code to form a final cyclic code represented by a polynomial R2(x) using the first transform, wherein R2(x) equals R1(x)/G1(x).