A Decoding Procedure which Improves Code Rate and Error Corrections
Shah · Journal of Advanced Research in Applied Mathematics · 2012
Corresponding to $C_{0}[n,n-r]$, a binary cyclic code generated by a primitive irreducible polynomial $p(X)\\in \\mathbb{F}_{2}[X]$ of degree $r=2b$, where $b\\in \\mathbb{Z}^{+}$, we can constitute a binary cyclic code $C[(n+1)^{3^{k}}-1,(n+1)^{3^{k}}-1-3^{k}r]$, which is generated by primitive irreducible generalized polynomial $p(X^{\\frac{1}{3^{k}}})\\in \\mathbb{F}_{2}[X;\\frac{1}{3^{k}}\\mathbb{Z}_{0}]$ with degree $3^{k}r$, where $k\\in \\mathbb{Z}^{+}$. This new code $C$ improves the code rate and has error corrections capability higher than $C_{0}$. The purpose of this study is to establish a decoding procedure for $C_{0}$ by using $C$ in such a way that one can obtain an improved code rate and error-correcting capabilities for $C_{0}$.