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On the construction of [q4+q2−q, 5,q4−q3+q2− 2q;q]-codes meeting the Griesmer bound

✍ Scribed by Noboru Hamada; Tor Helleseth; Øyvind Ytrehus

Publisher
Springer
Year
1992
Tongue
English
Weight
237 KB
Volume
2
Category
Article
ISSN
0925-1022

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✦ Synopsis

It is unknown whether or not there exists an [87, 5, 57 ; 31-code. Such a code would meet the Griesmer bound. The purpose of this paper is to give a constructive proof of the existence of [q4 + q2 _ q, 5, q'* -q3 + q2 _ 2q; q]-codes for any prime power q _> 3. As a special case, it is shown that there exists an [87, 5, 57; 3]-code with weight enumerator I + 156z 57 + 82z 60 + 2z ~s + 2z 78. The new construction settles an open problem due to Hill and Newton [10].

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