TY - JOUR

T1 - Linear hash functions and their applications to error detection and correction

AU - Ryabko, Boris

PY - 2023

Y1 - 2023

N2 - We describe and explore so-called linear hash functions and show how they can be used to build error detection and correction codes. The method can be applied for different types of errors (for example, burst errors). When the method is applied to a model where the number of distorted letters is limited, the obtained estimate of its performance is slightly better than the known Varshamov–Gilbert bound. We also describe random code whose performance is close to the same boundary, but its construction is much simpler. The proposed error correction codes are close to those obtained in the theory of linear codes, but there are examples when the proposed algorithms are more efficient.

AB - We describe and explore so-called linear hash functions and show how they can be used to build error detection and correction codes. The method can be applied for different types of errors (for example, burst errors). When the method is applied to a model where the number of distorted letters is limited, the obtained estimate of its performance is slightly better than the known Varshamov–Gilbert bound. We also describe random code whose performance is close to the same boundary, but its construction is much simpler. The proposed error correction codes are close to those obtained in the theory of linear codes, but there are examples when the proposed algorithms are more efficient.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85171765855&origin=inward&txGid=d6c44be0bf148988c7ba5a6dcf398e31

UR - https://www.mendeley.com/catalogue/ebe51fa3-bc64-360f-a6fa-7ad8f3a40510/

U2 - 10.1142/s1793830923500702

DO - 10.1142/s1793830923500702

M3 - Article

JO - Discrete Mathematics, Algorithms and Applications

JF - Discrete Mathematics, Algorithms and Applications

SN - 1793-8309

M1 - 2350070

ER -