The extended golay codes considered as ideals
نویسندگان
چکیده
منابع مشابه
Golay Codes
We discuss a specific type of error-control coding using Golay codes. First we introduce the basics of coding. Then we discuss the Golay code in binary form, extended binary form, and ternary form.
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 کاملConstructions of the Golay Codes: A Survey
1.1 Preliminaries A code of length n over the finite field Fq is a subset of V = F n q , and it is linear if it is an Fq-subspace of V . When q = 2 we talk of binary codes and binary linear codes. The weight w(a) of an element a ∈ V is the number of non-zero entries in a. The minimum weight of a linear code C is the smallest number which is a weight of a non-zero element of C. The weight enumer...
متن کاملOn Construction of the (24,12,8) Golay Codes
—Two product array codes are used to construct the (24, 12, 8) binary Golay code through the direct sum operation. This construction provides a systematic way to find proper (8, 4, 4) linear block component codes for generating the Golay code, and it generates and extends previously existing methods that use a similar construction framework. The code constructed is simple to decode.
متن کاملConstrained designs for maximum likelihood soft decoding of RM(2, m) and the extended Golay codes
AbstTactwe present algorithms for maximum likelihood soft decoding of the second order Reed-Muller codes RM(2,m) and the extended (24,12,8) Golay code. The decoding procedures are based on a concise representation of appropriately selected cosets of a subcode of the code considered. Such representation enables application of certain elimination rules. A structure, called constrained design, is ...
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: Journal of Combinatorial Theory, Series A
سال: 1990
ISSN: 0097-3165
DOI: 10.1016/0097-3165(90)90069-9