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2010•Unpublished venueRequires access

Undetected error probability of hamming code for any number of symbols

Manish K. Gupta, Jaskaran Bhullar, Bharat Naresh Bansal

Open publisher page 4 citations

Abstract

In past papers, it has been shown that probability of undetected error Pu(ε) for binary (n = 2m- 1, k = n - m, 3) Hamming code (q = 2) used for error detection on binary symmetric channel satisfies the 2-pbound, where p is the parity check bits equal to n - k, hence binary Hamming codes are proper. In this correspondence this result is generalized and it has been shown that not only binary but Hamming Codes (for any value of q) satisfy this bound, so generalized Hamming codes are proper.

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What this paper is about

In past papers, it has been shown that probability of undetected error Pu(ε) for binary (n = 2m- 1, k = n - m, 3) Hamming code (q = 2) used for error detection on binary symmetric channel satisfies the 2-pbound, where p is the parity check bits equal to n - k, hence binary Hamming codes are proper. In this correspondence this result is generalized and it has been shown that not only binary but Hamming Codes (for any value of q) satisfy this bound, so generalized Hamming codes are proper.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In past papers, it has been shown that probability of undetected error Pu(ε) for binary (n = 2m- 1, k = n - m, 3) Hamming code (q = 2) used for error detection on binary symmetric channel satisfies the 2-pbound, where p is the parity check bits equal to n - k, hence binary Hamming codes are proper. In this correspondence this result is generalized and it has been shown that not only binary but Hamming Codes (for any value of q) satisfy this bound, so generalized Hamming codes are proper.

Key concepts: Hamming distance, Hamming bound, Hamming code, Binary number, Hamming(7,4), Combinatorics, Discrete mathematics, Code (set theory)

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