Using polynomials over the GF(2) field for detecting and correcting errors in cyclic codes
Session
Computer Science and Communication Engineering
Description
Developments of the last decades in the field of digital communication have created a close connection between mathematics and computer engineering fields. The Galois field GF(2)={0,1} is of great use in Computer Science, along with the polynomials with coefficients from the field GF(2). If we denote by V(n,q) the vector space over the field GF(q), then the linear binary code C[n,k] is nothing but a subspace of the vector space V(n,q). The transmission of word codes through channels with obstacles of different natures, errors may occur, which we must detect and correct. Cyclic codes are an important group of linear binary codes. They are widely used in the theory of codes, since they are easily applied, particularly in their polynomial form. In this paper we will provide the algorithm for detecting and correcting errors that may occur in cyclic code.
Keywords:
Vector space, linear code, cyclic code, word code, detection, polynomials
Proceedings Editor
Edmond Hajrizi
ISBN
978-9951-550-50-5
Location
UBT Kampus, Lipjan
Start Date
29-10-2022 12:00 AM
End Date
30-10-2022 12:00 AM
DOI
10.33107/ubt-ic.2022.284
Recommended Citation
Berisha, Diellza; Imeri, Bukuri; Reqica, Mirlinda; Zekaj, Blinera; and Jusufi, Azir, "Using polynomials over the GF(2) field for detecting and correcting errors in cyclic codes" (2022). UBT International Conference. 293.
https://knowledgecenter.ubt-uni.net/conference/2022/all-events/293
Using polynomials over the GF(2) field for detecting and correcting errors in cyclic codes
UBT Kampus, Lipjan
Developments of the last decades in the field of digital communication have created a close connection between mathematics and computer engineering fields. The Galois field GF(2)={0,1} is of great use in Computer Science, along with the polynomials with coefficients from the field GF(2). If we denote by V(n,q) the vector space over the field GF(q), then the linear binary code C[n,k] is nothing but a subspace of the vector space V(n,q). The transmission of word codes through channels with obstacles of different natures, errors may occur, which we must detect and correct. Cyclic codes are an important group of linear binary codes. They are widely used in the theory of codes, since they are easily applied, particularly in their polynomial form. In this paper we will provide the algorithm for detecting and correcting errors that may occur in cyclic code.