### Table 2: Examples of cyclic codes over F2 + uF2

"... In PAGE 8: ... We present some examples of cyclic codes over R with good minimum distance properties in Tables 2 and 3. In Table2 , dLee corresponds to the exact minimum Lee distance. We have used the results from minimum distance tables of binary cyclic codes from [11] to compute the exact dLee.... ..."

### Table 3: Examples of cyclic codes over F2 + uF2 of length 127

"... In PAGE 8: ... We have used the results from minimum distance tables of binary cyclic codes from [11] to compute the exact dLee. The results in Table3 have been computed by the BCH-like bound in Theorem 7. Remark 1 The above theorem holds good in the Z4-cyclic codes context also.... ..."

### Table 1. Some Cyclic Codes and Their Corresponding Number of Terms Required for Decoding.

"... In PAGE 16: ... Although it is not listed in [25] as a majority decodable code, the above result confirms that BCH (15,2) can be decoded by majority logic. Table1 lists some cyclic codes and their corresponding number of terms required for decoding. To specify a code, the code length n, number of information bits k, the minimum distance d, the minimum distance guaranteed by the BCH bound dBCH, and the exponents of the roots of the generator polynomial are tabulated like that in [2].... In PAGE 17: ... That is, if a code is designed to correct t0 error, in some cases it may have a minimum distance d = dBCH gt; 2t0+1; that is not all correctable errors can be corrected by the algorithm. One example is the (21,7) code presented in Table1 . Thus the following comparison is made between a Meggitt decoder and a neural decoder.... In PAGE 18: ... In other words, efficient decoding structures of long length codes that can be found by the proposed approach are still limited by the available memory size and the affordable computation time. There are two ways to expand the practical value of the proposed approach to find larger length codes : First, longer codes can be constructed from the codes of Table1 by the techniques of interleaving. To get a (bn,bk) code from an (n,k) code, taking any b codewords from the original code and merge the codewords by alternating the symbols.... ..."

### Table 4: Working of Decoding algorithm for Example 2

"... In PAGE 13: ...Table4 illustrates the working of the algorithm for errors indicated in Theorem 9 and Lemmas 6 and 7. The algorithm can be extended to any cyclic codes over the ring Fp[u]=u2, where Fp is a prime eld.... ..."

### Table 1: Hensel lifts of generator polynomials of binary quadratic residue codes. The quaternary quadratic residue codes Q4, Q4, N4, N 4 are de ned to be the cyclic codes generated by the Hensel lifts of mQ(x), (x ? 1)mQ(x), mN(x), (x ? 1)mN(x) respectively. At this point it is useful to have a general result about idempotents of cyclic codes over Z4 that are generated by a single polynomial. Note that Calderbank and Sloane [16] have shown that every cyclic code over Z4 is of the form (f; 2g) where 2gj2f; when 2g = 2f, the cyclic code is generated by the single polynomial f. Lemma 3.1. Let g2 be the generator polynomial of a binary cyclic code (g2) and let g be the Hensel lift of g2.

"... In PAGE 12: ... A subscript 2a will indicate a code de ned over the ring Z2a. Table1 below lists the Hensel lift h(x) of the binary polynomials h2(x) = mQ(x) for p = 7; 17; 23; 31, and 47.... ..."

### Table 3: Examples of cyclic codes of length 7. The symbol quot;? quot; means that the code is optimal.

"... In PAGE 7: ...4.1 Length 7 Table3 presents all the 33 ?2 non trivial cyclic codes of length 7. The factorization of x7 +1 is f1f2f3 where f1 := x + 1; f2 := x3 + x + 1; f3 := x3 + x2 + 1.... ..."

### Table 4: Examples of cyclic codes of length 15. The symbol quot;? quot; means that the code is optimal.

"... In PAGE 7: ...4.2 Length 15 Table4 presents all good cyclic codes of length 15. The factorization of x15 + 1 is equal to f1f2f3f4f5, where f1 := x + 1; f2 := x2 + x + 1; f3 := x4 + x + 1; f4 = x4 + x3 + 1; f5 = x4 + x3 + x2 + x + 1.... ..."