Pongrácz, András (2020) Binary linear codes with near-extremal maximum distance. SIAM JOURNAL ON DISCRETE MATHEMATICS. ISSN 0895-4801 (print); 1095-7146 (online) (In Press)
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Abstract
Let C denote a binary linear code with length n all of whose coordinates are essential, i.e., for each coordinate there is a codeword that is not zero in that position. Then the maximum distance D is strictly bigger than n/2, and the extremum D=(n+1)/2 is attained exactly by punctured Hadamard codes. In this paper, we classify binary linear codes with D=n/2+1. All of these codes can be produced from punctured Hadamard codes in one of essentially three different ways, each having a transparent description.
| Item Type: | Article |
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| Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra |
| Depositing User: | Dr. András Pongrácz |
| Date Deposited: | 14 Sep 2020 12:33 |
| Last Modified: | 03 Apr 2023 06:54 |
| URI: | http://real.mtak.hu/id/eprint/113210 |
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