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INTERNATIONAL JOURNAL OF SCIENTIFIC DEVELOPMENT AND RESEARCH International Peer Reviewed & Refereed Journals, Open Access Journal ISSN Approved Journal No: 2455-2631 | Impact factor: 8.15 | ESTD Year: 2016 open access , Peer-reviewed, and Refereed Journals, Impact factor 8.15 |
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| Paper Title: | ELEMENTS OF MDS CODES VIA EXTENDED CAUCHY MATRICES |
| Authors Name: | Dr.Rajesh Kumar Saini , Dr.Binny Gupta |
| Unique Id: | IJSDR2301096 |
| Published In: | Volume 8 Issue 1, January-2023 |
| Abstract: | An (n,k,d) linear code over the finite field F = GF(q) is maximum- distance separable(MDS) if it attains the Singleton bound d ≤ n-k+1. A k × n matrix G over F is a generator matrix of an MDS code if and only if every k columns of G are linearly Independent. In most cases, error patterns with slightly more than D/2 error can be corrected by an (N, K) maximum- distance separable (MDS) code. Earlier the complexity of computation increased with number of additional errors, where a single error could be amended with an acceptable degree of computation. To fight out this problem Sudan’s algorithm (1997) more errors can be corrected, in addition to this provides proof that for a limited number of errors, the correct codeword is always on a very small list of possible transmitted words. The right codeword is always on a very small list of possible transmitted words. |
| Keywords: | Maximum- distance separable, transmitted words, codes, element |
| Cite Article: | "ELEMENTS OF MDS CODES VIA EXTENDED CAUCHY MATRICES", International Journal of Science & Engineering Development Research (www.ijsdr.org), ISSN:2455-2631, Vol.8, Issue 1, page no.583 - 586, January-2023, Available :http://www.ijsdr.org/papers/IJSDR2301096.pdf |
| Downloads: | 000337070 |
| Publication Details: | Published Paper ID: IJSDR2301096 Registration ID:203540 Published In: Volume 8 Issue 1, January-2023 DOI (Digital Object Identifier): Page No: 583 - 586 Publisher: IJSDR | www.ijsdr.org ISSN Number: 2455-2631 |
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