TY - JOUR

T1 - Bounds on the dimension of codes and subcodes with prescribed contraction index

AU - Vardy, Alexander

AU - Snyders, Jakov

AU - Be'ery, Yair

PY - 1990/12

Y1 - 1990/12

N2 - Let C be a linear code over GF(q), spanned by the rows of a matrix G of rank k. A nonnegative integer λ is said to be the contraction index of C if a maximal set of pairwise linearly independent columns of G has k + λ elements. We derive several upper and lower bounds on the dimension of a proper subcode of C with a prescribed contraction index v < λ. We also present an upper bound on the dimension of any linear code over GF(q) of length n, minimum Hamming distance d, and contraction index λ. For certain values of n and d the latter bound is shown to be tight for all q and λ. This substantially generalizes the results obtained by Delsarte and by Duc for λ = 1.

AB - Let C be a linear code over GF(q), spanned by the rows of a matrix G of rank k. A nonnegative integer λ is said to be the contraction index of C if a maximal set of pairwise linearly independent columns of G has k + λ elements. We derive several upper and lower bounds on the dimension of a proper subcode of C with a prescribed contraction index v < λ. We also present an upper bound on the dimension of any linear code over GF(q) of length n, minimum Hamming distance d, and contraction index λ. For certain values of n and d the latter bound is shown to be tight for all q and λ. This substantially generalizes the results obtained by Delsarte and by Duc for λ = 1.

UR - http://www.scopus.com/inward/record.url?scp=34648819176&partnerID=8YFLogxK

U2 - 10.1016/0024-3795(90)90269-I

DO - 10.1016/0024-3795(90)90269-I

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AN - SCOPUS:34648819176

SN - 0024-3795

VL - 142

SP - 237

EP - 261

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -