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Weight distribution of low-density periodic random errors and their correcting codes with error decoding probability | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2023. № 62. DOI: 10.17223/20710410/62/8

We present weight distribution of low-density periodic random errors in the space of all q-ary n-tuples along with the average Hamming weight of the error set. We also provide necessary and sufficient conditions for the existence of linear codes correcting such error pattern. Examples of such codes are given. Finally, probability of decoding error of such codes over a binary symmetric channel is derived.
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  • Title Weight distribution of low-density periodic random errors and their correcting codes with error decoding probability
  • Headline Weight distribution of low-density periodic random errors and their correcting codes with error decoding probability
  • Publesher Tomask State UniversityTomsk State University
  • Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 62
  • Date:
  • DOI 10.17223/20710410/62/8
Keywords
parity-check matrix, syndromes, periodic random error, error decoding probability
Authors
References
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Weight distribution of low-density periodic random errors and their correcting codes with error decoding probability | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2023. № 62. DOI: 10.17223/20710410/62/8
Weight distribution of low-density periodic random errors and their correcting codes with error decoding probability | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2023. № 62. DOI: 10.17223/20710410/62/8
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