A New Construction for the Extended Binary Golay Code
نویسندگان
چکیده
منابع مشابه
A New Construction for the Extended Binary Golay Code
We give a new construction of the extended binary Golay code. The construction is carried out by taking the Gray image of a self-dual linear code over the ring R = F2+uF2+vF2+uvF2 of length 6 and size 212. Writing a typical generating matrix of the form [I3|A], with A being a 3× 3 matrix over R, and finding some dependencies among the entries of A, we are able to set a general form for the gene...
متن کاملConstructing the Extended Binary Golay Code
Coding theory is the subject which is concerned with how information can be sent over a noisy channel. A code then is a collection of codewords which are strings of a fixed number of letters from an alphabet. Some of these strings are codewords others are not. When a codeword is sent over a channel there is a probability less than /2 that each letter in the codeword will be changed, thus introd...
متن کاملThe poset structures admitting the extended binary Golay code to be a perfect code
Brualdi et al. [Codes with a poset metric, Discrete Math. 147 (1995) 57–72] introduced the concept of poset codes, and gave an example of poset structure which admits the extended binary Golay code to be a 4-error-correcting perfect P-code. In this paper we classify all of the poset structures which admit the extended binary Golay code to be a 4-error-correcting perfect P-code, and show that th...
متن کاملThe Golay Code Outperforms the Extended Golay Code Under Hard-Decision Decoding
We show that the binary Golay code is slightly more power efficient than the extended binary Golay code under maximum-likelihood (ML), hard-decision decoding. In fact, if a codeword from the extended code is transmitted, one cannot achieve a higher probability of correct decoding than by simply ignoring the 24th symbol and using an ML decoder for the non-extended code on the first 23 symbols. T...
متن کاملHigh-Speed Decoding of the Binary Golay Code
Recently, some table-lookup decoding algorithms (TLDAs) have been used to correct the binary Golay code. This paper proposes an efficient high-speed TLDA called message-syndrome decoding algorithm (MSDA) by using the message syndrome to correct the binary systematic Golay code. The proposed MSDA is based on the novel message-syndrome lookup table (MSLT). The MSLT merely consists of 12 candidate...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics & Information Sciences
سال: 2014
ISSN: 1935-0090,2325-0399
DOI: 10.12785/amis/080107