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A class of p-ary (n, k, d) cyclic codes with block length n = p, dimension k = 2 and minimum Hamming distance d = n - k + 1 = p - 1 is introduced, where p denotes a prime. These codes are maximum distance separable repeated-single-root cyclic codes with generator polynomial g(x) = (x-1)p-2. The codebook has size p² and contains a subset S of p(p - 1)codewords having p distinct symbols each. The size of S is maximum for the given parameters and its codewords are useful for applications of coded modulation in power-line communications. [ABSTRACT FROM AUTHOR]

A class of p‐ary (n, k, d) cyclic codes with block length n = p, dimension k = 2 and minimum Hamming distance d = n − k + 1 = p − 1 is introduced, where p denotes a prime. These codes are maximum distance separable repeated‐single‐root cyclic codes with generator polynomial g(x) = (x‒1)p‒2. The codebook has size p2 and contains a subset 𝕊 of p(p ‒ 1)codewords having p distinct symbols each. The size of 𝕊 is maximum for the given parameters and its codewords are useful for applications of coded modulation in power‐line communications. [ABSTRACT FROM AUTHOR]

A condition is proven on the roots of the generator polynomial of a q-ary cyclic code of block length n which guarantees full cyclic order for all nonzero codewords. For such cyclic codes having n = qm – 1, a theorem is proven which allows to partition the set of all nonzero codewords into cyclic equivalence classes of order n. [ABSTRACT FROM AUTHOR]