New ternary linear codes

A search algorithm for linear codes: progressive dimension growth

“…All of these codes are over G F (5), and they improve the lower bounds on minimum distances of best-known linear codes. (The code in the last row does not improve the bound, so it is not numbered.…”

“…We have executed the algorithm over the finite fields G F(q), for q = 2, 3, 4, 5, 7, 8, 9. Although we have found many record-tiers over all fields, all record-breakers came from the field G F (5). The first column in the table contains the codes we constructed using PDG only.…”

New quasi-twisted codes over F11— minimum distance bounds and a new database

“…To improve the code, a new column is found to replace one presently in the code so that the minimum distance is increased. Later on, a stochastic optimization called tabu search has been used to construct good QC or QT codes by Gulliver and Östergård [11], and Daskalov et al [12]. In a more recent paper, Gulliver [16] used the tabu search to find good QT codes over F 11 .…”

“…They have been shown to contain many good linear codes. With the help of modern computers, many record-breaking QC and QT codes have been constructed [2,3,[8][9][10][11][12][15][16][17][18][19]. However, the problem still becomes intractable as the dimension and the block length of the code get large.…”

A database of linear codes over F_13 with minimum distance bounds and new quasi-twisted codes from a heuristic search algorithm

“…De Boer [16] constructed a self-dual [18,9,9] code and optimal codes with parameters [23,3,20] and [23,17,6] over F 13 . Newhart [26] studied the extended quadratic residue (QR) codes [18,9,9], [24,12,10] and [30, 15,12] over F 13 . Grassl and Gulliver [28] showed non-existence of a self-dual MDS code over F 13 with parameters [12,6,7].…”