Scholars@Duke publication: On a Pair of Dual Subschemes of the Hamming Scheme Hn(q)

On a Pair of Dual Subschemes of the Hamming Scheme Hn(q)

Publication , Journal Article

Calderbank, AR; Goethals, JM

Published in: European Journal of Combinatorics

January 1, 1985

We consider codes in the Hamming association scheme Hn(q) with interesting metric properties. We describe how a uniformly packed linear code C determines a pair of dual subschemes. The existence of this pair of subschemes is used to establish restrictions on the possible distances between codewords in the dual code C^⊥. These restrictions also apply to arbitrary codes with degree e + 1 and strength 2e or 2e + 1. An analogous result gives necessary conditions for the existence of non-linear uniformly packed codes. When q = 2 we determine the possible parameters of uniformly packed 2-error-correcting linear codes. © 1985, Academic Press Inc. (London) Limited. All rights reserved.

Duke Scholars

Author Robert Calderbank Computer Science

Published In

European Journal of Combinatorics

DOI

10.1016/S0195-6698(85)80004-4

ISSN

0195-6698

Publication Date

January 1, 1985

Volume

Issue

Start / End Page

133 / 147

Related Subject Headings

Computation Theory & Mathematics
4904 Pure mathematics
0101 Pure Mathematics

Citation

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Calderbank, A. R., & Goethals, J. M. (1985). On a Pair of Dual Subschemes of the Hamming Scheme Hn(q). European Journal of Combinatorics, 6(2), 133–147. https://doi.org/10.1016/S0195-6698(85)80004-4

Calderbank, A. R., and J. M. Goethals. “On a Pair of Dual Subschemes of the Hamming Scheme Hn(q).” European Journal of Combinatorics 6, no. 2 (January 1, 1985): 133–47. https://doi.org/10.1016/S0195-6698(85)80004-4.

Calderbank AR, Goethals JM. On a Pair of Dual Subschemes of the Hamming Scheme Hn(q). European Journal of Combinatorics. 1985 Jan 1;6(2):133–47.

Calderbank, A. R., and J. M. Goethals. “On a Pair of Dual Subschemes of the Hamming Scheme Hn(q).” European Journal of Combinatorics, vol. 6, no. 2, Jan. 1985, pp. 133–47. Scopus, doi:10.1016/S0195-6698(85)80004-4.

Calderbank AR, Goethals JM. On a Pair of Dual Subschemes of the Hamming Scheme Hn(q). European Journal of Combinatorics. 1985 Jan 1;6(2):133–147.

Published In

European Journal of Combinatorics

DOI

10.1016/S0195-6698(85)80004-4

ISSN

0195-6698

Publication Date

January 1, 1985

Volume

Issue

Start / End Page

133 / 147

Related Subject Headings

Computation Theory & Mathematics
4904 Pure mathematics
0101 Pure Mathematics