Journal of Xidian University ›› 2020, Vol. 47 ›› Issue (6): 158-163.doi: 10.19665/j.issn1001-2400.2020.06.022

• Information and Communications Engineering & Cyberspace Security • Previous Articles     Next Articles

Simple proof the generalized Helberg codes being capable of correcting insertion/deletion errors

MA Guochen1(),JIAO Xiaopeng1,MU Jianjun1,HAN Hui1,GUO Junjun2   

  1. 1. School of Computer Science and Technology, Xidian University, Xi’an 710071, China
    2. School of Computer Science and Engineering, Xi’an Technological University, Xi’an 710021, China
  • Received:2019-12-24 Online:2020-12-20 Published:2021-01-06

Abstract:

Since the existing proof method of the error correction capability for generalized Helberg codes is complicated, a simple proof that generalized Helberg codes are capable of correcting multiple insertion/deletion errors is proposed. By making a detailed analysis of the monotonicity of the inner product between the codeword and the weights for the generalized Helberg codes, the upper and lower bounds of the difference of the inner product between any two different codewords and weights are proved. By using the upper and lower bounds, the existing proof method for the error correction capability for generalized Helberg codes is simplified. The proposed simple proof is helpful in understanding generalized Helberg codes and making a further study.

Key words: error-correcting codes, insertion/deletion errors, Helberg codes, generalized Helberg codes

CLC Number: 

  • TN911.22