Coding Theory
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Matrix Ring Isomorphism Enables Cyclic Code Construction over F_16
The paper constructs cyclic codes over F_16 using the 4x4 matrix ring R = M_4(F_2[u]/<u^k>) over the truncated polynomial ring. It proves R isomorphic to a noncommutative ring F_16 + v F_16 + ... + v^3 F_16 + u (F_16 + ... ) + ... + u^{k-1} (...), with v^4 = u^k = 0 and commuting u^i v^j. Cyclic cod…