Binomial coefficient codes over W2)
نویسندگان
چکیده
Diaconis, P. and R. Graham, Binomial coefficient codes over GF(2) Discrete Mathematics 106/107 (1992) 181-188. In this note we study codes over GF(2) which are generated for given d and r by binary vectors of the form ((y), (,‘), , ({), . , (*‘i ‘)) (mod 2), 0 <i =Z d. We describe the weight enumerators of these codes and the numbers of codewords of weights 1 and 2. These results can be used to obtain sharp bounds on the rates of convergence to uniformity for certain random walks on the n-cube GF(2)“.
منابع مشابه
Testing k-binomial equivalence
Two words w1 and w2 are said to be k-binomial equivalent if every non-empty word x of length at most k over the alphabet of w1 and w2 appears as a scattered factor of w1 exactly as many times as it appears as a scattered factor of w2. We give two different polynomial-time algorithms testing the k-binomial equivalence of two words. The first one is deterministic (but the degree of the correspond...
متن کاملBinomial moments for divisible self-dual codes
For self-dual codes with all weights divisible by an integer greater than one, the minimum distance is bounded by the Mallows-Sloane upper bounds and by their improvements due to Krasikov-Litsyn and Rains. We obtain the improved upper bounds from short relations with constant coefficients on suitable binomial moments of the codes. In this approach, the Mallows-Sloane bounds are analogues of the...
متن کاملOn the Parameters of Codes with Two Homogeneous Weights
Delsarte showed that for any projective linear code over a finite field GF (p) with two nonzero Hamming weights w1 < w2 there exist positive integers u and s such that w1 = p u and w2 = p (u + 1). Moreover, he showed that the additive group of such a code has a strongly regular Cayley graph. Here we show that for any proper, regular, projective linear code C over a finite Frobenius ring with tw...
متن کاملAN OVERPARTITION ANALOGUE OF THE q-BINOMIAL COEFFICIENTS
We define an overpartition analogue of Gaussian polynomials (also known as q-binomial coefficients) as a generating function for the number of overpartitions fitting inside the M ×N rectangle. We call these new polynomials over Gaussian polynomials or over q-binomial coefficients. We investigate basic properties and applications of over q-binomial coefficients. In particular, via the recurrence...
متن کاملConstructing two-weight codes with prescribed groups of automorphisms
We are interested in the construction of linear [n, k; q] two-weight codes. A linear code is a k−dimensional subspaceC of the n−dimensional vector spaceGF (q) over the finite fieldGF (q) with q elements. The q codewords of length n are the elements of the subspace, they are written as row vectors. The weight of a codeword c is the number of nonzero components of the vector c ∈ GF (q). In the ca...
متن کامل