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Further classifications of codes meeting the Griesmer bound (Corresp.)

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For any(n, k, d)binary linear code, the Griesmer bound says thatn geq sum_{i=0}^{k-1} lceil d/2^{i} rceil, wherelceil x rceildenotes the smallest integergeq x. We consider codes meeting the Griesmer bound with equality. These codes have parametersleft( s(2^{k} - 1) - sum_{i=1}^{p} (2^{u_{i}} - 1), k, s2^{k-1} - sum_{i=1}^{p} 2^{u_{i} -1} right), wherek > u_{1} > cdots > u_{p} geq 1. We characterize all such codes whenp = 2oru_{i-1}-u_{i} geq 2for2 leq i leq p.

Published in:

Information Theory, IEEE Transactions on  (Volume:30 ,  Issue: 2 )

Date of Publication:

Mar 1984

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