Hourglass of constant weight

Ternary Constant Weight Codes

Let A3(n, d,w) denote the maximum cardinality of a ternary code with length n, minimum distance d, and constant Hamming weight w. Methods for proving upper and lower bounds on A3(n, d,w) are presented, and a table of exact values and bounds in the range n ≤ 10 is given.

Optimal Constant Weight Codes

A new class of binary constant weight codes is presented. We establish new lower bound and exact values on A(n, 2k, k + 1), in particular, A(30, 12, 7) = 9, A(48, 16, 9) = 11, A(51,16, 9) = 12, A(58, 18, 10) = 12. An ( ) w d n , , constant weight binary code is a code of length n , code distance d in which all code words have the same number of “ones” . The number of “ones” is w . We will denot...

Constant-Weight Array Codes

Binary constant-weight codes have been extensively studied, due to both their numerous applications and to their theoretical significance. In particular, constant-weight codes have been proposed for error correction in store and forward. In this paper, we introduce constant-weight array codes (CWACs), which offer a tradeoff between the rate gain of general constant-weight codes and the low deco...

The sedimentation constant, diffusion constant and molecular weight of lactoglobulin.

Arithmetic progressions with constant weight

Let k ≤ n be two positive integers, and let F be a field with characteristic p. A sequence f : {1, . . . , n} → F is called k-constant, if the sum of the values of f is the same for every arithmetic progression of length k in {1, . . . , n}. Let V (n, k, F ) be the vector space of all kconstant sequences. The constant sequence is, trivially, k-constant, and thus dim V (n, k, F ) ≥ 1. Let m(k, F...