### Table 1: Projection of binary linear codes onto GF(4)

2003

"... In PAGE 8: ... In this way we obtain optimal binary [28; 15; 6] codes having projection O or projection E onto a linear [7; 4; 3] code over GF(4). See Table1 for more codes, where the fourth column denotes the highest minimum weight of the corresponding binary [n; k] code together with the theoretical upper bound. Example 4.... In PAGE 8: ... We get several optimal binary codes having projection O or projection E on C4. See Table1 for more examples. 5 Projections of binary self-dual codes onto GF(4) In this section, we characterize binary self-dual codes of length 8k which have either projec- tion O or projection E.... In PAGE 12: ...xample 5.5. When k = 2, there are exactly two Type II [16; 8; 4] binary codes A8 apos; A8 and E16 in the notation of [19]. By using exactly two Type II additive quaternary (4; 24; 2) codes in [15, Table1 ] or [13], we see that A8 apos; A8 and E16 have projection E onto (4; 24; 2) codes. The Type I [16; 8; 4] binary code F16 has projection E onto the Type I (4; 24; 2) code in [15, Table 2] or [13].... ..."

### Table 5: Parameters of generalized Gray image of extended Hensel lift of QR(n) (left) and minimum distance of the best known linear codes of same length and size (right).

2003

"... In PAGE 6: ... Following this work, we lifted generating polynomial of QR(n) for n = 17, 23, 31, 47 to Z8 and Z16, extended the resulting codes by a parity-check sym- bol, then computed their minimum distance with computer assistance. Results are shown in Table5 , bold (resp. italic) is for codes better than (resp.... ..."

Cited by 1

### Table 4.1 Projection of binary linear codes onto GF(4).

### Table II. Here, three linear output neurons are used in order to enable binary coding. Every output signal is then converted into binary digits as shown. Table III represents the data describing the new ANN used for diagnosis.

### Table 1. Isometry Classes of Optimal Indecomposable Binary Codes

2006

"... In PAGE 12: ... [4], Chapter 7), we refine the problem by requiring that the minimum distance of the codes searched for be high. As a result of the search, the author determined the number of isometry classes of optimal indecomposable binary linear codes as presented in Table1 . For small n and k, the table indicates the optimal minimum distance of binary (n, k)-codes as well as the number of isometry classes (in the exponent).... ..."

### Table 1: Minimal length f2(K) of any [N; K; D] binary intersecting code. The entries for K 6 are exact while the remaining entries give upper bounds on f2(K). Explicit codes are known in every case.

"... In PAGE 7: ...issing, the following entry should be used. Explicit arrays are known in every case. It follows from (12) that the entries in Table 3 for n 11 are exact. However, the author expects that most of the other entries (as well as those in Table1 ) can be considerably improved, and o ers these tables as a challenge to the reader. Acknowledgements I should like to thank David Applegate, Aart Blokhuis, Andries Brouwer, G erard Cohen, John Conway, Bill Cook, J anos Korner, Donald Kreher, Simon Litsyn, Colin Mallows, Klaus Metsch and Vladimir Tonchev, all of whom have contributed to this paper.... In PAGE 12: ...[49] shows that f(K) = c2K(1+o(1)) can be achieved by Goppa codes (although his argument is also nonconstructive). Table1 gives the best upper bounds presently known on f2(K) for small values of K. For K 6 the values of f2(K) are easily proved to be optimal, using Theorems 1(i), 2(ii), 2(iii), and the bounds on the minimal distance of binary linear codes given in [58].... In PAGE 12: ...Two of the best codes in Table1 are duals of BCH codes. It seems likely that the duals of some longer BCH codes will also provide good intersecting codes.... In PAGE 12: ... 280) to guarantee that the weights satisfy condition (iii), but unfortunately the resulting codes are quite weak. Generator matrices for some of the other codes mentioned in Table1 are given in Table 2. If the generator matrix has the form [A I] then Table 2 gives the rows of A in hexadecimal.... In PAGE 12: ... If the generator matrix has the form [A I] then Table 2 gives the rows of A in hexadecimal. The remaining codes in Table1 may be obtained from the author.... ..."

### Table 1: Minimal length f2(K) of any [N; K; D] binary intersecting code. The entries for K 6 are exact while the remaining entries give upper bounds on f2(K). Explicit codes are known in every case.

"... In PAGE 7: ...issing, the following entry should be used. Explicit arrays are known in every case. It follows from (12) that the entries in Table 3 for n 11 are exact. However, the author expects that most of the other entries (as well as those in Table1 ) can be considerably improved, and o ers these tables as a challenge to the reader. Acknowledgements I should like to thank David Applegate, Aart Blokhuis, Andries Brouwer, G erard Cohen, John Conway, Bill Cook, J anos Korner, Donald Kreher, Simon Litsyn, Colin Mallows, Klaus Metsch and Vladimir Tonchev, all of whom have contributed to this paper.... In PAGE 12: ...[49] shows that f(K) = c2K(1+o(1)) can be achieved by Goppa codes (although his argument is also nonconstructive). Table1 gives the best upper bounds presently known on f2(K) for small values of K. For K 6 the values of f2(K) are easily proved to be optimal, using Theorems 1(i), 2(ii), 2(iii), and the bounds on the minimal distance of binary linear codes given in [58].... In PAGE 12: ...Two of the best codes in Table1 are duals of BCH codes. It seems likely that the duals of some longer BCH codes will also provide good intersecting codes.... In PAGE 12: ... 280) to guarantee that the weights satisfy condition (iii), but unfortunately the resulting codes are quite weak. Generator matrices for some of the other codes mentioned in Table1 are given in Table 2. If the generator matrix has the form [A I] then Table 2 gives the rows of A in hexadecimal.... In PAGE 12: ... If the generator matrix has the form [A I] then Table 2 gives the rows of A in hexadecimal. The remaining codes in Table1 may be obtained from the author.... ..."

### Table 1: Maximum Minimum Lee Distances for Best Self-Orthogonal (pm, m) QC Codes over Z4

"... In PAGE 15: ... It was found that it is best to first find a code with a specified even minimum distance, then check for orthogonality. Table1 presents the minimum weights of the best codes obtained. Note that it was shown in [18] that self-dual QT codes exist only for lengths a multiple of 8 (m a multiple of 4).... In PAGE 15: ... Note that it was shown in [18] that self-dual QT codes exist only for lengths a multiple of 8 (m a multiple of 4). The first rows of the twistulant matrices of the QT codes listed in Table1 are compiled in Tables 2 - 5. Since this is the first compiled table of Z4 codes (self-orthogonal or otherwise), it is not possible to compare these codes with previous results.... In PAGE 15: ... However, using the Gray map, it is possible to compare these codes with the best binary linear codes [3] with even minimum distance. Of the 111 entries in Table1 , 54 or almost half attain the best known distance for the corresponding binary code. Hence the class of self-orthogonal QT codes contains many good codes.... ..."