Code pairs with specified parity of the Hamming distances
نویسندگان
چکیده
For code pairs (A, B); A, B C {0, 1 ..... 7-1}"; with mutually constant parity of the Hamming distances a conjecture of the first author concerning the maximal value of IAIIBI is established.
منابع مشابه
Pairs of codes with prescribed Hamming distances and coincidences
The main problem of coding theory is to construct codes with large Hamming-distances between the code-words. In this work we describe a fast algorithm for generating pairs of q-ary codes with prescribed pairwise Hamming-distances and coincidences (for a letter s 2 f0; 1; : : : ; q 1g, the number of s-coincidences between codewords a and b is the number of letters s in the same positions both in...
متن کاملThe Graph, Geometry and Symmetries of the Genetic Code with Hamming Metric
The similarity patterns of the genetic code result from similar codons encoding similar messages. We develop a new mathematical model to analyze these patterns. The physicochemical characteristics of amino acids objectively quantify their differences and similarities; the Hamming metric does the same for the 64 codons of the codon set. (Hamming distances equal the number of different codon posi...
متن کاملBinary set functions and parity check matrices
We consider the possibility of extending to a family of sets a binary set function defined on a subfamily so that the extension is, in fact, uniquely determined. We place in this context the problem of finding the least integer n(r) such that every linear code of length n with n B n(r), dimension n r and minimum Hamming distance at least 4 has a parity check matrix composed entirely of odd weig...
متن کاملBinary Convolutional Codes of High Rate
The function N(r; ; dfree), defined as the maximum n such that there exists a binary convolutional code of block length n, dimension n r, constraint length , and free distance dfree, is studied. For dfree 2 f3; 4g, codes are obtained from simple constructions that determine N(r; ; dfree) for all positive integers and r. Codes with minimum Hamming distance dfree 5 are found by computer search. A...
متن کاملOn the erasure-correcting capabilities of low-complexity decoded LDPC codes with constituent Hamming codes
Low-density parity-check (LDPC) codes can be constructed using constituent block codes other than single parity-check (SPC) codes. This paper considers random LDPC codes with constituent Hamming codes and investigates their asymptotic performance over the binary erasure channel. It is shown that there exist Hamming code-based LDPC codes which, when decoded with a low-complexity iterative algori...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 188 شماره
صفحات -
تاریخ انتشار 1998