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In the extended binary Golay code, all code words have Hamming weights of 0, 8, 12, 16, or 24. Code words of weight 8 are called octads and code words of weight 12 are called dodecads. Octads of the code G 24 are elements of the S(5,8,24) Steiner system. There are 759 = 3 × 11 × 23 octads and 759 complements thereof.
However, do note that a shift operand value which is either a negative number or is greater than or equal to the total number of bits in this value results in undefined behavior. For example, when shifting a 32 bit unsigned integer, a shift amount of 32 or higher would be undefined. Example:
A bitwise AND is a binary operation that takes two equal-length binary representations and performs the logical AND operation on each pair of the corresponding bits. Thus, if both bits in the compared position are 1, the bit in the resulting binary representation is 1 (1 × 1 = 1); otherwise, the result is 0 (1 × 0 = 0 and 0 × 0 = 0).
In a binary tree the balance factor of a node X is defined to be the height difference ():= (()) (()) [6]: 459 of its two child sub-trees rooted by node X. A node X with () < is called "left-heavy", one with () > is called "right-heavy", and one with () = is sometimes simply called "balanced".
Following are some examples, with illustrations of the cases C 3 = 5 and C 4 = 14. Lattice of the 14 Dyck words of length 8 – (and ) interpreted as up and down. C n is the number of Dyck words [6] of length 2n. A Dyck word is a string consisting of n X's and n Y's such that no initial segment of the string has more Y's than X's. For example ...
If n is a power of two, then the coded value for 0 ≤ x < n is the simple binary code for x of length log 2 (n). Otherwise let k = floor(log 2 (n)), such that 2 k < n < 2 k+1 and let u = 2 k+1 − n. Truncated binary encoding assigns the first u symbols codewords of length k and then assigns the remaining n − u symbols the last n − u ...
A Hamiltonian cycle on a tesseract with vertices labelled with a 4-bit cyclic Gray code. Every hypercube Q n with n > 1 has a Hamiltonian cycle, a cycle that visits each vertex exactly once. Additionally, a Hamiltonian path exists between two vertices u and v if and only if they have different colors in a 2-coloring of the graph.
Golay code may refer to: Binary Golay code, an error-correcting code used in digital communications; Ternary Golay code (Golay) complementary sequences