Weight Spectrum of Codes Associated With the Grassmannian G(3,7)

作者：Kaipa Krishna V^*; Pillai Harish K

来源：IEEE Transactions on Information Theory, 2013, 59(2): 986-993.

DOI：10.1109/TIT.2012.2219497

• Grassmannian
• Pfaffian
• trilinear alternating forms
• weight spectrum

In this paper, we consider the problem of determining the weight spectrum of q-ary codes C(3, m) associated with Grassmann varieties G(3, m) For, m = 6, this was done in a paper by Nogin in 1997. We derive a formula for the weight of a codeword of C(3, m), in terms of certain varieties associated with alternating trilinear forms on F-q(m). The classification of such forms under the action of the general linear group GL(m, F-q) is the other component that is required to calculate the spectrum of C(3, m). For, m = 7, we explicitly determine the varieties mentioned above. The classification problem for alternating three-forms on F-q(7) was solved in a study by Cohen and Helminck in 1988, which we then use to determine the spectrum of C(3, 7).

• 出版日期2013-2