WebA general algebraic method for decoding all types of binary cyclic codes is presented. It is shown that such a method can correct t=[(d-1)/2] errors, where d is the true minimum … WebWe deal with the minimum distances of q -ary cyclic codes of length q m - 1 generated by products of two distinct minimal polynomials, give a necessary and sufficient condition for …

On the minimum distance of ternary cyclic codes

Web2 de mai. de 2024 · 1 Answer Sorted by: 1 The question should be the minimum distance is at least 4. (NTU final exam,right?) Suppose f ( x) is a nonzero codeword in C with weight at most 3, say f = a x i + b x j + c x k, where 0 ≤ i < j < k < n . Since g ( x) f ( x), then f ( α) = f ( α 2) = f ( α 3) = 0, so a α i l + b α j l + c α k l = 0, l = 1, 2, 3. WebKeywords: Finite elds, cyclic codes, trace representations, permutation polynomials. Abstract Estimation of the minimum distance of cyclic codes is a classical problem in … minecraft xbox one frame rate

On some bounds on the minimum distance of cyclic codes over …

WebSection 4 focuses on lower bounds for the minimum sum-rank distance of a cyclic-skew-cyclic code. We provide the analogues of the Roos bound and of the Hartmann-Tzeng bound, exploiting the notion of defining sets for cyclic-skew-cyclic codes. In Section 5 we focus on tensor products of codes. We combine a cyclic code in the Hamming WebSince every linear code is contained in an MDS linear code with the same minimum distance over some finite field extension, we focus our study on MDS linear codes. It is … Web26 de abr. de 2024 · We can thus conclude that the minimum distance of this code is d m i n = 6. It may be worth observing that because x + 1 is a factor of the generator, all the … morva mckenzie scottish athletics