For a given binary BCH code Cn of length n = 2s-1 generated by a polynomial g(x)e{open}F2[x] of degree r there is no binary BCH code of length (n + 1)n generated by a generalized polynomial g(x1/2)e{open}F2[x1/2ℤ ≥ 0] of ...

For a given binary BCH code Cn of length n = 2s-1 generated by a polynomial g(x)e{open}F2[x] of degree r there is no binary BCH code of length (n + 1)n generated by a generalized polynomial g(x1/2)e{open}F2[x1/2ℤ ≥ 0] of ...

Currently, there has been an increasing demand for operational and trustworthy digital data transmission and storage systems. This demand has been augmented by the appearance of large-scale, high-speed data networks for ...

Currently, there has been an increasing demand for operational and trustworthy digital data transmission and storage systems. This demand has been augmented by the appearance of large-scale, high-speed data networks for ...

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 ...

This study establishes that for a given binary BCH code C0 n of length n generated by a polynomial g(x) ∈ F2[x] of degree r there exists a family of binary cyclic codes {Cm 2m−1(n+1)n}m≥1 such that for each m ≥ 1, the ...