On complete decoding of linear error-correcting codes
نویسندگان
چکیده
منابع مشابه
Decoding error-correcting codes via linear programming
Error-correcting codes are fundamental tools used to transmit digital information over unreliable channels. Their study goes back to the work of Hamming [Ham50] and Shannon [Sha48], who used them as the basis for the field of information theory. The problem of decoding the original information up to the full error-correcting potential of the system is often very complex, especially for modern c...
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The problem of decoding up to error correcting capacity of arbitrary linear codes with the use of Gröbner bases is addressed. A new method is proposed, which is based on reducing an initial decoding problem to solving some system of polynomial equations over a finite field. The peculiarity of this system is that, when we want to decode up to half the minimum distance, it has a unique solution e...
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Error-correcting codes are fundamental tools used to transmit digital information over unreliable channels. Their study goes back to the work of Hamming [Ham50] and Shannon [Sha48], who used them as the basis for the field of information theory. The problem of decoding the original information up to the full error-correcting potential of the system is often very complex, especially for modern c...
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Error correcting output codes (ECOC) represent a successful extension of binary classifiers to address the multiclass problem. Lately, the ECOC framework was extended from the binary to the ternary case to allow classes to be ignored by a certain classifier, allowing in this way to increase the number of possible dichotomies to be selected. Nevertheless, the effect of the zero symbol by which d...
متن کاملList decoding of error correcting codes
Error-correcting codes are combinatorial objects designed to cope with the problem of reliable transmission of information on a noisy channel. A fundamental algorithmic challenge in coding theory and practice is to efficiently decode the original transmitted message even when a few symbols of the received word are in error. The naive search algorithm runs in exponential time, and several classi...
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ژورنال
عنوان ژورنال: Information and Control
سال: 1980
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(80)90526-4