| \`x^2+y_1+z_12^34\` |
{{journal.titleEn}} {{journal.titleEn}} {{journal.titleEn}} Department of Mathematics, University of Rijeka, Radmile Matejčić 2, 51000 Rijeka, Croatia
Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield 0002, Pretoria, South Africa
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, Building S8, 9000 Ghent, Belgium
In this paper we construct $ 2 $-PD-sets of $ 16 $ elements for codes from the Desarguesian projective planes $ \mathrm{PG}(2,q) $, where $ q = 2^h $ and $ 5\leq h \leq 9 $. We also construct $ 3 $-PD-sets of $ 75 $ elements for the code from the Desarguesian projective plane $ \mathrm{PG}(2,q) $, where $ q = 2^9 $. These $ 2 $-PD-sets and $ 3 $-PD-sets can be used for partial permutation decoding of codes obtained from the Desarguesian projective planes.
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Table 1. Codes of
| $ q $ | Code | $ t $ | $ r $ | $ b $ | $ b_2 $ |
| $ 32 $ | [1057,244, 33] | 16 | 813 | 180 | 3 |
| $ 64 $ | [4161,730, 65] | 32 | 3431 | 1623 | 3 |
| $ 128 $ | [16513, 2188,129] | 64 | 14325 | 40696 | 3 |
| $ 256 $ | [65793, 6562,257] | 128 | 59231 | 3965945 | 3 |
| $ 512 $ | [262657, 19684,513] | 256 | 242973 | 3625171287 | 3 |
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