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Hamming Code
, 2006
"... corrects all single bit errors (in a codeword consisting of either 64-bit data and 8 parity bits, or 32-bit data and 7 parity bits), and it detects double bit errors in the data. This design utilizes Hamming code, a simple yet powerful method for ECC operations. As a result, this design offers excep ..."
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corrects all single bit errors (in a codeword consisting of either 64-bit data and 8 parity bits, or 32-bit data and 7 parity bits), and it detects double bit errors in the data. This design utilizes Hamming code, a simple yet powerful method for ECC operations. As a result, this design offers
On partitions into nonparallel Hamming codes
"... Abstract. Let F denote the finite field with two elements. We describe a con-struction of partitions of Fn, for n = 2m − 1,m ≥ 4, into cosets of pairwise distinct Hamming codes (we call such codes nonparallel) of length n. We give a lower bound for the number of different such partitions. 1 ..."
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Abstract. Let F denote the finite field with two elements. We describe a con-struction of partitions of Fn, for n = 2m − 1,m ≥ 4, into cosets of pairwise distinct Hamming codes (we call such codes nonparallel) of length n. We give a lower bound for the number of different such partitions. 1
SYNCHRONIZATION OF HAMMING CODES
"... Abstract — In this report we investigate the symbol and frame synchronization of a (7,4) Hamming code with BPSK modulation and zero mean AWGN. A matched filter instead of a product integrator or correlator has been used to establish symbol synchronization by identifying the shape of the received pul ..."
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Abstract — In this report we investigate the symbol and frame synchronization of a (7,4) Hamming code with BPSK modulation and zero mean AWGN. A matched filter instead of a product integrator or correlator has been used to establish symbol synchronization by identifying the shape of the received
Decoding the Hamming code
"... A friend thinks of an integer between 0 and 15. You are allowed to ask seven yes/no-questions in order to determine which number your friend has in mind. However, he is allowed to tell at most one lie. Can you do this task? The theory of error correcting codes says that you can do it. In fact, this ..."
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, this problem is solved by the Hamming code of length 7, with 4 information bits [2]. However, the practical question remains, can you find the number while standing on your feet together with your friend. This note presents seven question cards and one base card allowing you to do this feat. Each card encodes
Design and Implementation of Hamming Code on
"... information theory, error detection and correction has great practical importance in maintaining information integrity across noisy channels. Error coding is considered as a method of detecting and correcting these errors to ensure that the information is transferred intact from its source to its de ..."
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destination. There are various error correcting techniques to detect and correct the error. One of the popular technique based on forward error correction is Hamming Code. This paper focuses on design and its hardware implementation on Field programmable Gate Array(FPGA). The design includes both
Weight Distributions of Hamming Codes (II)
, 2007
"... In a previous paper, we derived a recursive formula determining the weight distributions of the [n = (q m − 1)/(q − 1), n −m,3] Hamming code H(m,q), when (m, q −1) = 1. Here q is a prime power. We note here that the formula actually holds for any positive integer m and any prime power q, without ..."
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In a previous paper, we derived a recursive formula determining the weight distributions of the [n = (q m − 1)/(q − 1), n −m,3] Hamming code H(m,q), when (m, q −1) = 1. Here q is a prime power. We note here that the formula actually holds for any positive integer m and any prime power q, without
Hamming codes are rate-efficient array codes
- in Proc. IEEE Global Telecomm. Conf
, 2005
"... Array codes are error-correcting codes of very low complexity that were initially used for burst and erasure correction in Redundant Arrays of Inexpensive Disks (RAID) architectures and other storage applications. The structure of these codes allows a very simple encoding and decoding mechanism. Alt ..."
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. Although they are very high-rate codes, they do not achieve the maximum possible rate given their design constraints. In fact Hamming codes maximize the possible rate given these design constraints. This paper compares the rate and complexity of array codes when compared to Hamming codes. Keywords: Array
Optimization of the Hamming Code for Error Prone Media
"... This paper proposes an optimized version of the Hamming code. The paper begins with identifying a seed that can be used as basis to generate Hamming codes. It then shows that starting with a message that is only two bits long, along with three parity bits; one can add extra message bits incrementall ..."
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This paper proposes an optimized version of the Hamming code. The paper begins with identifying a seed that can be used as basis to generate Hamming codes. It then shows that starting with a message that is only two bits long, along with three parity bits; one can add extra message bits
On permutation automorphism groups of q-ary Hamming codes
"... Abstract. It is established that for any q> 2 the permutation automorphism group of a q-ary Hamming code of length n = (qm − 1)/(q − 1) is isomorphic to the unitriangular group UTm(q). 1 ..."
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Abstract. It is established that for any q> 2 the permutation automorphism group of a q-ary Hamming code of length n = (qm − 1)/(q − 1) is isomorphic to the unitriangular group UTm(q). 1
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