Year: 2020
Type: preprint
Abstract: The current best known $[239, 21], \, [240, 21], \, \text{and} \, [241, 21]$ binary linear codes have minimum distance 98, 98, and 99 respectively. In this article, we introduce three binary Goppa codes with Goppa polynomials $(x^{17} + 1)^6, (x^{16} + x)^6,\text{ and } (x^{15} + 1)^6$. The Goppa codes are $[239, 21, 103], \, [240, 21, 104], \, \text{and} \, [241, 21, 104]$ binary linear codes respectively. These codes have greater minimum distance than the current best known codes with the respective length and dimension. In addition, with the techniques of puncturing, shortening, and extending, we find more derived codes with a better minimum distance than the current best known codes with the respective length and dimension.
Source: arXiv (Cornell University)
Institution: University of Puerto Rico System
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3092815408