منابع مشابه
How many weights can a linear code have?
We study the combinatorial function L(k, q), the maximum number of nonzero weights a linear code of dimension k over Fq can have. We determine it completely for q = 2, and for k = 2, and provide upper and lower bounds in the general case when both k and q are ≥ 3. A refinement L(n, k, q), as well as nonlinear analogues N(M, q) and N(n,M, q), are also introduced and studied.
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We prove a complex polynomial of degree n has at most ⌈n/2⌉ attractive fixed points lying on a line. We also consider the general case.
متن کاملHow many runs can a string contain?
Given a string x = x[1..n], a repetition of period p in x is a substring ur = x[i+1..i+rp], p = |u|, r ≥ 2, where neither u = x[i+1..i+p] nor x[i+1..i+(r+1)p+1] is a repetition. The maximum number of repetitions in any string x is well known to be Θ(n log n). A run or maximal periodicity of period p in x is a substring urt = x[i+1..i+rp+ |t|] of x, where ur is a repetition, t a proper prefix of...
متن کاملHow Many Squares Can a String Contain?
All our words (strings) are over a fixed alphabet. A square is a subword of the form uu=u, where u is a nonempty word. Two squares are distinct if they are of different shape, not just translates of each other. A word u is primitive if u cannot be written in the form u=v j for some j 2. A square u with u primitive is primitive rooted. Let M(n) denote the maximum number of distinct squares, P(n)...
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We show that a protein can be trained to recognize multiple conformations, analogous to an associative memory, and provide capacity calculations based on energy fluctuations and information theory. Unlike the linear capacity of a Hopfield network, the number of conformations which can be remembered by a protein sequence depends on the size of the amino acid alphabet as lnA, independent of prote...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2020
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2019.2946660